Sindbad~EG File Manager

/*  6.17.13,  problems read from difhigh.mhw */
char *problems141[] = {
"1. y = t^3 - 4t^2 + 2",
"2. y = x^5 - x^3 + 1",
"3. y = 6x^3 - 7x^5",
"4. f(x) = x^3 + 3x^2 + 6x",
"5. f(x) = x^8 - x^6 + x^4 - x^2 + 1",
"6. y = ax^2 + bx + c",
"7. y = (1 - 2t) (1 +t)",
"8. y = x^4 - 3x^3 + 2x^2 - x +1",
"9. y = 5x^3 - 3x^5 - 7",
"10. y = 3 (t^2 + t)^2",
"11. y = (2x^2 + x +1)^10",
"12. y = x^n",
"13. y = ((x^3) / 3) + ((x^2) / 2) + x +1",
"14. y = ((-t)^2) ^5",
"15. y = 1 / (x - 1)",
"16. y = 1 / (x^2 - 1)",
"17. y = 1 / (x - 7)",
"18. y = (x^2 - 4) / x",
"19. y = x/(1+ x)",
"20. y = (x + 2) / (2x + 1)",
"21. y = (x + 4) / (x^2 + 1)",
"22. y = (x + 1/x)^3",
"23. y = (x^2 +1) (x^(- 2) - 1)",
"24. y = x^3 + x^(- 3)",
"25. y = sqrt x",
"26. y = sqrt(3t + 1)",
"27. y = root (3, x)",
"28. y = root (4, x)",
"29. y = root (5, x)",
"30. y = x^(5/2)",
"31. f(x) = sqrt x - 10",
"32. y = x^(1/2) + x^(1/4)",
"33. y = x^(1/3) - x^(- 1/3)",
"34. y = x^(3/2) + 2x^(1/2)",
"35. y = root (3, 3x^2)",
"36. y = 1 /  root (3, 7 - x)",
"37. f(t) = sqrt (t + sqrt t)",
"38. y = sqrt (1+x^3)",
"39. y = root (3, 1 - u^2)",
"40. y = (1+sqrt t) / (5t)",
"41. y = (1 - x^2)^(5/2)",
"42. h(x) =sqrt(x^2 + 1)",
"43. G(r) = sqrt(r) + root(3, r)",
"44. y = sin x",
"45. y = cos x",
"46. y = tan x",
"47. y = cot x",
"48. y = sec x",
"49. y = csc x",
"50. y = sin (3x)",
"51. y = cos (2x)",
"52. y = sin x + cos x",
"53. y = 5 tan (x/3)",
"54. y = cot (2x - 1)",
"55. y = 1 / (sin x) + 1/ (cos x)",
"56. y = sin x (cos x)",
"57. y = cos(3x)",
"58. y = sin^2 (2x - 1)",
"59. y = sin^3 (3x)",
"60. y = cos^4 (4x)",
"61. y = tan^3(2t)",
"62. y = x^4 + cot^2 (x)",
"63. y = (abs x) x",
"64. y = x^2 (abs x)",
"65. y = ln x",
"66. y = e^(x^2)",
"67. y = e^(x^2 - 1)",
"68. y = 1 / (e^x - 1)",
"69. y = ln (e^x - 1)",
"70. y = x^2 (ln x)",
"71. y = ln (x^2 + x + 1)",
"72. y = e^(sin x - 1)",
"73. y = x^(pi)",
"74. y = (1-x^2)^(3/4)",
"75. H(t) = tan^3(2t-1)",
"76. F(r) = sec(sqrt r)",
""};

/*  6.17.13,  problems read from difimpl.mhw */
char *problems142[] = {
"1. y^3=x^2",
"2. x^2-3xy=18",
"3. y^2=x^2+2x",
"4. x^3 + y^3 = 1",
"5. x^3 +xy -y^3 = 9",
"6. x^2 y^3 =1",
"7. x^2y^2=9",
"8. (x-1)y^2=x+1",
"9. x^2 y^3 +y^2 x^3 + x +1=0",
"10. 1/x + 1/y = 3+x+y",
"11. x^2 - 6x/y + y^2 = 7",
"12. y/(x-y) = 2x^3",
"13. 1/(x+1)+1/(y+1)=1",
"14. 1/x^2+1/y^2=20",
"15. (xy+y^3)/(1+x)=1",
"16. 2x + y - xy^(3/2) = 4",
"17. x^2+sqrt (xy)=7",
"18. 2/x + xy^(3/2) = 4(x-y)",
"19. x^(-1)+sqrt (x-y)= xy",
"20. sqrt x+(1/sqrt y)=2",
"21. sqrt x + sqrt y =1",
"22. (x^2+y^2)^2=4xy",
"23. (x^2+y^3)^3=8x^2y^2",
"24. y-1=sqrt(1-sqrt x)",
"25. x=sqrt ((x^4-x+1)^3)+xy",
"26. x=e^y",
"27. e^(xy)= 1",
"28. e^xy=2x+y",
"29. x-y^2=e^(y^2)",
"30. xe^(xy)=2",
"31. 2e^(x^2 y)=x",
"32. ln(x-y)=xy",
"33. ln(x-y/x)=x+y",
"34. x^4 = x^2 - y^2",
"35. y+sqrt y ln x=x^2+y^2",
"36. x sin y = 1",
"37. x cos y = sin y",
"38. y^2=x cos y",
"39. tan xy=x",
"40. (sin x)(cos y)=y",
"41. (sin x)(cos y)=x",
"42. sin x -cos^2 y =x+y",
"43. x=sin^2(y)",
"44. y^2 =1-x^2 sec y",
"45. x^2=sin (y^2)",
"46. x+y=(sin y) / (cos x)",
"47. xy = tan(x/y)",
"48. y^2=sin ((x+5))^(5/4)",
"49. sin (sqrt y)-3x=2",
"50. sqrt(xy) + ln(x+y) = 1",
""};

/*  6.17.13,  problems read from relrate.mhw */
char *problems143[] = {
"1. 3y = 14x^2, diff(x,t) = - 6, x=1",
"2. A = pi r^2,  diff(A,t) = 1 , r = 3",
"3. y = 4x^2+100, diff(x,t) = 10 , x=10",
"4. V = x^3, diff(x,t) = 3 , x = 20",
"5. V = (4/3) pi r^3, diff(V,t) = 100 , r = 50",
"6. xy = 1, diff(x,t) = 4 , x = 2",
"7. S = 6x^2, diff(x,t) = 3 , x = 20",
"8. V = 36 pi h, diff(V,t) = 8  ,  h = 2",
"9. W = 100 (1+r / 4000)^(-2), diff(r,t) = 15 , r = 400",
"10. y = 2x^3 - 3x^2+4, diff(x,t) =2 , x = 2",
"11. V = 16 x, diff(V,t) = 2 , x =1",
"12. D = sqrt (y^2+900), diff(y,t) = 15 , y = 30",
"13. S = u^3, diff(u,t) = -2 , u = 3",
"14. V = (4/3)pi R^3, diff(V,t) = 20 pi , R = 10",
"15. V = pi R^2 h / 3, diff(R,t) = 5, diff(h,t) = -6 , R = 4, h = 3",
"16. y = 3 sqrt (x+9), diff(x,t) = 2 , x=7",
"17. P = 3 / W, diff(P,t) = 5 , P =9",
"18. y = sqrt x - 4, diff(y,t) = 3 , x= 4",
"19. xy = 1, diff(x,t) = 2 , x =1",
"20. xy = -8, diff(x,t) = 2 , x = 4",
"21. A = xy / 2, diff(x,t) = 4, diff(y,t) = -3 , x = 20, y = 12",
"22. A = xy, diff(A,t) = 4, diff(x,t) = 1/2  , A = 800, y=200",
"23. D = sqrt (16+y^2), diff(D,t) = 3600 , y = 5",
"24. x^2 + 3xy + y^2 = 1, diff(y,t) = -2 , y= -1, x=0",
"25. V = (4/3)pi r^3, diff(V,t) = -2, r=3       @ The volume of a sphere is decreasing at 2 cubic meters/second.  At what rate is the radius decreasing when the radius is 3?",
"26. xy^2+4y - 44 = 0, diff(x,t) = 3 , y = 2",
"27. y = 4x^2 - 100, diff(y,t) = -6 , x = 1",
"28. 4x^2+y^2 = 25, diff(x,t) = 5 , x = 3/2, y = 4",
"29. 4x^2+y^2 = 25, diff(x,t) = 5, x = 3/2, y = -4",
"30. y - x^2+4x = -10, diff(y,t) = 3 , x = -2",
"31. x^2+xy+y = 16, diff(y,t) = 5 , x = 4",
"32. u^2 = x^2+(90)^2, diff(x,t) = 20, x = 30, u = -30 sqrt (10)",
"33. 48 S - 480 = S h, diff(h,t) = 32, S = 30, h = 32",
"34. y^2 = (30+x)^2 - (18)^2, diff(y,t) = 9, x = 6, y = 18 sqrt 3",
"35. y = 1 / (x^2 - 1), diff(y,t) = 1, x = -2",
"36. 2 y^3 - x^2+4x = -10, diff(y,t) = -3, x = -2, y = 1",
"37. A = 2 h sqrt (16+h^2), diff(A,t) = 2 , h = 3",
"38. A = x (600 - x) / 2, diff(A,t) = 4 , x = 200",
"39. x^2+y^3+z^4 = -3, diff(x,t) = -3, diff(z,t) = 4 , x = 2, y = -2, z = 1",
"40. xyz = 10, diff(x,t) = -2, diff(z,t) = 3, x = 2, y = -5, z = -1",
"41. V = 4 pi r^3 / 3, S = 4 pi r^2, diff(V,t) = 10 , r = 4",
"42. x = 20 tan theta, diff(x,t) = 4 , x = 15",
"43. y - x = sin y, diff(x,t) = 3 , y = pi / 2",
"44. h = 20 tan theta, diff(h,t) = 3 , theta = pi/6",
"45. L = 40 sec theta - 20 tan theta+ 30, diff(L,t) = -1 , theta = pi / 4",
"46. A = ( r  theta) / 2 - (sin theta) / 2, diff(r,t) = 1,  diff(A,t) = -1 , theta = pi/2, A = 1/4",
""};

/*  6.17.13,  problems read from minmax.mhw */
char *problems144[] = {
"1. f(x) = (10-x)x, -infinity < x < infinity",
"2. f(x) = x(x+1),-infinity < x < infinity",
"3. f(x) = 1+3x, -1 <= x",
"4. f(x) = 4x+1, x <= 6",
"5. f(x) = abs(x), -3 <= x <= 2",
"6. f(x) = abs(3x-1), 0 <= x <= 2",
"7. f(x) = 1-x^2, 0 < x < 1",
"8. f(x) = 1-x^2, 0 < x <= 1",
"9. f(x) = 1-x^2, 0 <= x < 1",
"10. f(x) = 1-x^2, 0 <= x <= 1",
"11. f(x) = 1-x^2, -2 <= x <= 1",
"12. f(x) = 1+(x+1)^2, -3 <= x <4",
"13. f(t) = 1/t, 0 < t < 1",
"14. f(t) = 1/t, 0 < t <= 1",
"15. f(theta) = sin theta, -2pi <= theta <= 2pi",
"16. f(theta) = tan theta, -pi/4 <= theta < pi/2",
"17. f(theta) = cos(theta/2), -pi < theta < pi",
"18. f(theta) = sec theta, -pi/2 < theta <= pi/3",
"19. f(x) = x^5, -1 <= x <= 1",
"20. f(x) = 2-x^4, -1 <= x <= 1",
"21. f(x) = x^2 - 2x+ 2, 0 <= x <= 3",
"22. f(x) = 1-2x-x^2, -4 <= x <= 1",
"23. f(x) = x^3-x, -1 <= x <= 1",
"24. f(x) = 4x^3-15x^2 + 12x + 7, -2 <= x <= 1",
"25. f(x) = 2x^3 + 3x^2 + 4, -2 <= x <= 1",
"26. f(x) = 18 x + 15x^2 -4x^3, -3 <= x <= 4",
"27. f(x) = x^4 - 4x^2 + 2, -3 <=x <=2",
"28. f(x) = 3x^5 - 5x^3 - 1, -2 <= x <= 2",
"29. f(x) = x^2 + x/2, 1/2 <= x <= 2",
"30. f(x) = sqrt(9-x^2), -1 <= x <= 2",
"31. f(x) = x^(4/5), -32 <= x <= 1",
"32. f(x) = x/(x+1), 1 <= x <= 2",
"33. f(x) = abs(x-1)-1, -1 <= x <= 2",
"34. f(x) = abs(x^2 + x), - 2 <= x <= 1",
"35. f(x) = x(1-x),  x >= 0",
"36. f(x) = x/(1-x), x >= 2",
"37. f(x) = sin x + cos x, 0 <= x <= pi/3",
"38. f(x) = x - 2 cos x, -pi <= x <= pi",
"39. f(x) = x^3-12x+1, -3<=x <=5",
"40. f(x) = x^4-x^2,-infinity < x < infinity",
"41. f(x) = x^5-x^2, -1 <= x <= 1",
"42. f(x) = 2sin(x)-x, 0 <= x <= pi",
"43. f(x) = 1/(1+x^2),-infinity < x < infinity",
"44. f(x) = e^(-x^2),-infinity < x < infinity",
"45. f(x) = e^sin(x),  0 <= x <= pi",
"46. f(x) = e^x + e^(-x),-infinity < x < infinity",
"47. f(x) = 1/x + 1/(1-x), 0 < x < 1",
"48. f(x) = 2/x + 1/(1-x), 0 < x < 1",
"49. f(x) = 1/(x^2 + 1) + 1/((x-1)^2 + 1), 0 <= x <= 1",
"50. f(x) = 1/((x+10)^2 + 1) + 1/((x-10)^2 + 1), -12 <= x <= 12",
""};

/*  6.17.13,  problems read from limrat.mhw */
char *problems145[] = {
"1. lim(x-> 3, (6 - 2x) / (x - 3))",
"2. lim(t-> 0, t (1 - 1/t))",
"3. lim(x-> 1, (x^2 - 1) / (1 - x))",
"4. lim(x-> -1, (x^2 - 1) / (3x+3))",
"5. lim(x-> 2, (x - 2) / (x^3 - 8))",
"6. lim(x-> -1, (x^3 - 1) / (x+1))",
"7. lim(x-> 2, (3x - 6) / (x^3 - 2x^2))",
"8. lim(y-> 1/2, (6y - 3) / (y(1 - 2y)))",
"9. lim(y-> 1, (1 - y) / (1 - y^3))",
"10. lim(x-> -1, ((3+3x) / (x^3+1))^3)",
"11. lim(t-> -5, (t+5) / (t^2 - 25))",
"12. lim(x-> 1, (x^2 - 1) / (x^3 - 1))",
"13. lim(x-> 1, (x^5 - 1) / (x^3 - 1))",
"14. lim(u-> -1, (u^4 - 1) / (u^3+1))",
"15. lim(x-> 1, ((x - 1)^2) / (x^2 - 1))",
"16. lim(x-> 2, (x^2+x - 2) / (x^2 - 4))",
"17. lim(x-> 2, (x - 2) / (x^2 - 5x+6))",
"18. lim(u-> 1, (u^2 - 2u+1) / (u^2 - 1)^2)",
"19. lim(u-> 2, (u^2 - 7u+10) / (u^6 - 64))",
"20. lim(x-> 1, (x - 2) / (x^2 - 10x+25))",
"21. lim(x-> 1, (x^2 - x) / (x^3 - x^2+x - 1))",
"22. lim(x-> 4, (x^3+4x^2+x+4) / (x^2+3x - 4))",
"23. lim(u-> -1, (u^4+1) / (u^3 - 1))",
"24. lim(x-> 2, ((x^2 - 4x+3) / (x^2 - 4x+4))^4)",
"25. lim(t->1/2, (2t^2+5t - 3) / (6t^2 - 7t+2))",
"26. lim(u-> 2, (1/u^2 - 1/4) / (u - 2))",
"27. lim(x-> 2, (1/x - 1/2) / (x - 2))",
"28. lim(x-> 0, (1+1/x) / (1+1/x^2))",
"29. lim(x-> 2, (x / (x+1) - 2/3) / (x - 2))",
"30. lim(x-> 1+sqrt 2, ((x - 1)^4 - 4) / ((x - 1)^2 - 2))",
"31. lim(t-> sqrt 3, (t^4 - 6t^2+9) / (t^2 - 3))",
"32. lim(x-> 1, (x^2+x - 2) / (x^5 - 1))",
"33. lim(x-> -3, (x+3) / (1/3+1/x))",
"34. lim(x-> 1, (1 / (x - 1)) - x^2 / (x - 1))",
"35. lim(x-> 1, (x^2+x - 2) / (x - 1))",
"36. lim(x->-1, (x^2+6x+5) / (x^2+3x+2))",
"37. lim(u-> - 4, (2u / (u+4)) - 8 / (u+4))",
"38. lim(y-> infinity, (1 - y) / (1 - y^3))",
"39. lim(x-> infinity, ((1 - x)(2 - 3x)) / (10x^2 - 4))",
"40. lim(x->infinity,(x - 4)/(x^2-2x - 1))",
"41. lim(x-> infinity, (2x^2+x - 1) / (7x^2+3))",
"42. lim(t->infinity,(7t^3+3t)/(2t^3+t^2+1))",
"43. lim(t-> infinity, t^3 / (t - 3) - t^2)",
"44. lim(t->-infinity,(7t^2 + 5t)/((1+t)(2t+3)))",
"45. lim(x-> infinity, (2x^2+x - 1) / (x^3+3))",
"46. lim(x->infinity, (x^5-1)/(x^6 - 1))",
"47. lim(x-> infinity, (3x^2 - x+5) / ((5 - 4x)(1 - 3x)))",
"48. lim(x->infinity, (x-2)(x-3)^2 / ((x-4)^2(x+5)))",
"49. lim(x-> - infinity, ((x+4)(x+1)) / ((2x+7)(x+2)))",
"50. lim(x->infinity, (x-2)(x-3)^2(x-4)^2 / ((x+5)(x+6)^2(x+7)^2))",
"51. lim(x-> infinity, 1/x + 2x / (x+1))",
"52. lim(x-> infinity, (x^2+1) / x^4)",
"53. lim(x-> infinity, (7x - 10) / (x (x+1)))",
"54. lim(u-> infinity, (u^3 - u - 2) / (2u^3+u^2+1))",
""};

/*  6.17.13,  problems read from limatinf.mhw */
char *problems146[] = {
"1. lim(x-> -infinity, 5x^(-1/3))",
"2. lim(y-> infinity, 1/y^2 + 1/y^4 + 1)",
"3. lim(x->infinity,sqrt(1+x)-sqrt x)",
"4. lim(y-> infinity,1/(y sqrt y))",
"5. lim(x-> infinity, 3x/ sqrt (4x^2+1))",
"6. lim(x-> infinity, (sqrt x) / (4 sqrt x - x))",
"7. lim(x-> -infinity, (8+x^2) / (x (x - 1))^(1/3))",
"8. lim(x->infinity, (x - sqrt x)/(x + sqrt x))",
"9. lim(x-> infinity, x^3 - 1/x^3)",
"10. lim(x-> infinity, x^2/(x+1) - x^2/(x - 1))       @It would not be correct to replace the denominators by their leading term $x$."
  " That would give zero, which is not the correct answer."
  " This shows that leading terms must be used with care!"
"11. lim(x->infinity,root(3, 1+x)-root(3, x))",
"12. lim(x-> infinity, sqrt (x^2-16) / (x - 4))",
"13. lim(x-> infinity, (4x - 1) / sqrt (16x^2+1))",
"14. lim(x-> infinity, 2x - sqrt (4x^2 - 1))",
"15. lim(t-> infinity, t / (t^(1/2) + 2t^(-1/2)))",
"16. lim(x-> infinity,sqrt((x^2-1)/(x+7x^2)))",
"17. lim(x-> infinity,1/(5 + sqrt x))",
"18. lim(x-> infinity,sqrt(1+x)-sqrt(x-1))",
"19. lim(x-> infinity, sqrt(x^2+x -1) + x)",
"20. lim(x-> -infinity,root(3, x+1) - root(3, x - 1))",
"21. lim(x-> infinity, x - sqrt x)",
"22. lim(x-> infinity, sqrt (x^2/(1+3x^2)))",
"23. lim(x-> infinity, (x^2 + x) / (x^3+x^2))",
"24. lim(x-> infinity, x^3/(x - 5) - x^2)",
"25. lim(x-> infinity, x - 1/x + x^2 - 1/x^2)",
"26. lim(x-> infinity, (7x - 10) / sqrt(x (x+1)))",
"27. lim(x-> -infinity, x / sqrt (4x^2+1))",
"28. lim(x-> infinity, sqrt(x) / (x^2 - 1))",
"29. lim(x-> infinity, 3 sqrt (x^2/4 - 1) - 3x/2)",
"30. lim(x-> infinity, sqrt(4 + x^2)/(4+x))",
"31. lim(x-> infinity,sqrt(x^2+3x)/(- x+1))",
"32. lim(x-> infinity, (1+ sqrt x)/(1- sqrt x))",
"33. lim(x-> infinity, sqrt(x^2+x - 1) -x)",
"34. lim(x-> infinity, sqrt x / (4 sqrt x + 1))",
"35. lim(x-> infinity, sqrt (x+50) - x)",
"36. lim(x-> infinity, sqrt (1+x^2) / x)",
"37. lim(x-> infinity, x^(3/5) - x^(5/3))",
"38. lim(x-> infinity, root(3, x^2+8)/(x+1))",
"39. lim(x-> -infinity, root(3, x^3+8)/(x - 1))",
"40. lim(u-> infinity, (u^3 - sqrt(u) - 2) / (2u^3+u^2+1))",
"41. lim(x-> infinity, 1/x + 5x/(x+1))",
"42. lim(x-> infinity, (abs x) / sqrt (x^2+1))",
"43. lim(y-> infinity, (9y^3 - y) / (y^3 +1))",
"44. lim(x-> infinity, (x+2) / (x+3) - (x^3+2) / (x^3+3))",
"45. lim(x-> -infinity, sqrt ((3 - x) / (1 - x)))",
"46. lim(x-> infinity, x + sqrt(x^2+2x+1))",
"47. lim(x-> infinity, sqrt(x^2 - 1)-sqrt(x^2+1))",
"48. lim(x-> infinity, (x^(4/3) - x^(1/3) +1) / (3x^(4/3)+3))",
"49. lim(t-> infinity, cos(1/t))",
"50. lim(x-> infinity, cos^2 x)",
"51. lim(x-> infinity, 1/ (sec x - 1))",
"52. lim(x-> infinity, (1 - cos x) / x^2)",
"53. lim(x-> infinity, (cos x) / sqrt (x^2 - 1))",
"54. lim(x-> infinity, e^(-1/x))",
"55. lim(x-> infinity, e^(-x^2))",
"56. lim(x-> infinity, ln (- ln (1/x)))",
"57. lim(x-> infinity, x sin(1/x^2))",
"58. lim(x-> infinity, x sqrt (4x^2 -1) / sqrt (9x^3 -1))",
"59. lim(x-> infinity, (16 - x^2)^(1/3) / (4 - x))",
""};

/*  6.17.13,  problems read from inflimit.mhw */
char *problems147[] = {
"1. lim(x->0, 1/x^6)",
"2. lim(x->0, 1/x^6 - 1/x^4)",
"3. lim(x->3, 1/(x-3)^8)",
"4. lim(x-> 0, 1+1/x)",
"5. lim(x->5+,1/(x-5))",
"6. lim(x-> -7+, sqrt (x+7))",
"7. lim(x->infinity, x - sqrt x)",
"8. lim(x-> infinity, x^3+x^2 - x - 1)",
"9. lim(t-> 0, sqrt (1/t^2))",
"10. lim(x-> 0, 10/x^(1/5))",
"11. lim(y-> 0+, y^(- 1/5))",
"12. lim(x-> 0+, 3/(x^2 - 3x))",
"13. lim(x-> 0+, (x^2 - 1) / x)",
"14. lim(x-> 5, 1 / (x - 5)^3)",
"15. lim(x-> 0- , (x^2 - 1) / x)",
"16. lim(x->infinity, x - x^3)",
"17. lim(x->-infinity, root(3, x^2))",
"18. lim(x-> infinity, sqrt(x^3+x+1) / (x^2+sqrt(x)+1))",
"19. lim(x-> 0, (1/x+x^2) / (x^2+1))",
"20. lim(x-> 1+ , (x^3 - 1) / (x - 1)^3)",
"21. lim(x-> 2, (x^3 - 8)^2 / (x^2 - 4)^3)",
"22. lim(x->-3+, x^2/(x^2 + 5x+6))",
"23. lim(x-> - 1- , (x^4 - 1) / (x+1)^2)",
"24. lim(x-> 1, (x^2 - x+1) / (5x - 5))",
"25. lim(x-> 1, (x^2+x+1) / (x^2 - 1))",
"26. lim(x->0, (x+1)/x^2 - (x-1)/x^2)",
"27. lim(x-> infinity, x / (x+1)+x^3 / (x^2+1))",
"28. lim(x-> 0+, sqrt x + 1/ sqrt x)",
"29. lim(x-> 2+ , 1 / sqrt (x^2 - 4))",
"30. lim(x-> 2-, x / sqrt (4 - x^2))",
"31. lim(x-> infinity, sqrt x + 1 / sqrt x)",
"32. lim(x-> 5- , sqrt (x / (5 - x)))",
"33. lim(x-> 3- , sqrt (9 - x^2) / (x - 3))",
"34. lim(x-> infinity, root(3, (9+x^3) / (x(x+1))))",
"35. lim(x-> infinity, sqrt (9+x^2) - root (4, x))",
"36. lim(x-> 1+, 1/(sqrt (x^2 - x) + x))",
"37. lim(x-> 0- , 1/ abs x)",
"38. lim(x-> - 2+ , abs (x / (2+x)))",
"39. lim(x-> 1- , (x+1) / abs (x - 1))",
"40. lim(t->(pi/2)+, sec t)",
"41. lim(x-> pi/2 , sec^2 x)",
"42. lim(x-> pi/2- , csc (2x))",
"43. lim(x-> pi/2- , 10 / cos x)",
"44. lim(x-> 0, (cos x) / x)",
"45. lim(theta-> pi, theta / sin^2 theta)",
"46. lim(theta->pi/2-, (tan theta) / theta)",
"47. lim(x-> pi/2, (1 - cos x) / cos x)",
"48. lim(x-> 1, (sin x) / (x (x^2 - 1)))",
"49. lim(x-> infinity, x cos (1 / x^2))",
"50. lim(x-> 0, x sin (1/x^2))",
"51. lim(t-> 1- , ln (1 - abs t))",
"52. lim(x-> 1+ , ln (ln x ))",
"53. lim(x->infinity, (sqrt x + 3)/(x+3))",
"54. lim(x->infinity, x/sqrt(x-1))",
"55. lim(x->infinity, (sqrt x)/ root(3, x))",
"56. lim(x->0, ((x+1)/x^2)^2 - ((x-1)/x^2)^2)       @Each term goes to infinity, so you have to combine them before evaluating the limit.",
"57. lim(x-> - 1/4+ , (x - 1) / (4x+1))",
"58. lim(x-> 1/2+ , (4x - 3) / (x - 1/2))",
"59. lim(t-> infinity, root (3,t) sin (1/t))",
""};

/*  6.17.13,  problems read from intsigma.mhw */
char *problems148[] = {
"1. sum(1,i,1,7)",
"2. sum((-1+k/2),k,1,6)",
"3. sum((3 + j),j,1,3)",
"4. sum(k(k-1),k,1,10)",
"5. sum((i-3)(i+2),i,2,7)",
"6. sum(2(n-1),n,1,3)",
"7. sum((1-m/10),m,1,10)",
"8. sum((i/14)^2,i,1,7)",
"9. sum(k/2(3 + k/2),k,1,8)",
"10. sum((i^2-5),i,-3,3)",
"11. sum((j^2+2j),j,1,20)",
"12. sum((m^2-3m+1),m,-2,1)",
"13. sum(i(i-2),i,3,6)",
"14. sum(1/5(n/5)^3,n,1,5)",
"15. sum(1/5(k/5)^2,k,1,5)",
"16. sum(k^3,k,1,5)",
"17. sum(k^4,k,1,10)",
"18. sum((i+i^2-i^3),i,1,8)",
"19. sum((3i^3+i),i,1,10)",
"20. sum(i(i-1)(i-2),i,1,8)",
"21. sum(1/(n+1),n,1,5)",
"22. sum(1/(k-1),k,2,8)",
"23. sum(1/k(k+1),k,1,10)",
"24. sum(5i/(i+1),i,1,5)",
"25. sum(1/i^2,i,1,8)",
"26. sum((i-1)/(i+1),i,1,4)",
"27. sum((i+1)(i-1)/i,i,1,6)",
"28. sum(2^i , i,0,4)",
"29. sum(sqrt i,i,1,5)",
"30. sum( 1 +(-1)^i,i,1,10)",
"31. sum(i/6(-1)^i,i,1,6)",
"32. sum((-1)^i/(i-1),i,2,6)",
"33. sum((-1)^i/(i+1),i,1,5)",
"34. sum(cos(i pi/6),i,1,6)",
"35. sum(sin(i 2pi/6),i,0,5)",
"36. sum((-1)^i cos(i pi/2),i,0,5)",
"37. sum( cos(k pi), k,0,8)",
"38. sum(3^i,i,0,4)",
"39. sum(3^(-i),i,1,5)",
"40. sum(2^i/(i+1),i,0,10)",
"41. sum(1-5i,i,1,n)",
"42. sum(k/n,k,1,n)",
"43. sum(x^k,k,5,8)",
"44. sum(j/n^2,j,1,n)",
"45. sum(k^2/n^3,k,1,n)",
"46. sum(3i^2+i,i,1,n)",
"47. sum((3+2k)^2,k,1,n)",
"48. sum(i^3+2i^2+i+1,i,1,n)",
"49. sum((2+i/n)(2/n),i,1,n)",
"50. sum((-1)^n,n,1,20)",
""};

/*  6.17.13,  problems read from intpoly.mhw */
char *problems149[] = {
"1. integral (7, x)",
"2. integral (7, x, -1, 1)",
"3. integral (3x+4, x)",
"4. integral ( 3x - 1,x,0, 2)",
"5. integral (t/2 - 2, t, -2, 2)",
"6. integral (x^2, x, -1, 1)",
"7. integral( x^2,x,0,t)",
"8. integral (x^3, x, -1, 1)",
"9. integral( x^2,x,0, sqrt(t))       @The square root term is a constant.",
"10. integral (x^2+1, x, 0, 1)",
"11. integral( (x^2 + 2x + 1),x)",
"12. integral (3x^2+4, x, -2, 2)",
"13. integral (9t^2 - 3t+4, t)",
"14. integral (x^2+2x+1, x, 1, 3)",
"15. integral( x^2+x+1,x,1,4)",
"16. integral( 3x^2-6x+5,x)",
"17. integral (x^2+2x+1, x, -3, -1)",
"18. integral( x^2+4x+4,x,0, 9)",
"19. integral( (x^2 + 2x + 1),x)       @Don't factor the integrand.",
"20. integral( 5x^3-3x^2-x+5,x)",
"21. integral (6 - x - x^3, x)",
"22. integral (x^3 - x^2 + x - 7, x, -1, 2)",
"23. integral (1 - x - x^2 - 3x^3, x)",
"24. integral (a x^2 - x^3, x, 0, a)",
"25. integral (4x^3 - 6x^2 - 4x, x, -1, 2)",
"26. integral (2t^3 - t^2 - 3t+6, t, -2, 0)",
"27. integral (3t^3 - 2t - 1, t)",
"28. integral (u^3 - u, u, -x, x)",
"29. integral (3x^4 - 6x+6, x)",
"30. integral (3v^5 - 5v^5, v)",
"31. integral (x^4+2x^2+1, x, -1, 2)",
"32. integral (x^7 - 3x^4 + 3, x)",
"33. integral( x^33 -2x^11 -1,x)",
"34. integral ((7x - 1)^2, x)",
"35. integral ((3x+1)^2, x)",
"36. integral ((x+1)^4, x)       @Expand the integrand.",
"37. integral ((x+1)^4, x, -2, 0)       @Expand the integrand.",
"38. integral ((2x + 1)^3, x)",
"39. integral ((x+1)(x - 3), x, -2, 2)       @Multiply out the integrand.",
"40. integral (x(x^2+8), x)       @Multiply out the integrand.",
"41. integral ((x - 1)(4x^2 - 3), x)",
"42. integral (3x^2(x^3+1), x)",
"43. integral (2x(x^2+1), x, 1, 4)       @Multiply out the integrand.",
"44. integral ((x^2 + 3)(x^2 - 3), x)",
"45. integral ((x^2+2x+1)^2, x, -3, -1)",
"46. integral( (x^2-1)/(x-1),x)       @Factor the numerator and cancel.",
"47. integral( (x^3-1)/(x-1),x)       @Factor the numerator and cancel.",
"48. integral ((x^4 - 1) / (x^2+1), x)       @This simplifies to a polynomial,",
"49. integral ((x^6 - 1) / (x^2 - 1), x)       @This simplifies to a polynomial.",
"50. integral ((x^6+1) / (x^2+1), x)       @This simplifies to a polynomial.",
""};

/*  6.17.13,  problems read from intsimpl.mhw */
char *problems150[] = {
"1. integral (x^(3/5), x, 1, 32)",
"2. integral (1 - 2x+3x^2, x, 0, 2)",
"3. integral ( 5y^4 -6y^2 + 14,y,-3,3)",
"4. integral ( u^2 - u, u, -x, x)",
"5. integral (1 / x^5, x, -3, -1)",
"6. integral (1/y^3+10/y^4+1/y^5, y)",
"7. integral ((x^3+1) / x^2, x)",
"8. integral( 1/t^2 + 1/t^4,t,1, 2)",
"9. integral (1 / sqrt x, x ,1, 2)",
"10. integral ((t - 4) sqrt t, t)",
"11. integral ((x+1/x)^2, x)",
"12. integral( root(4, x^5) + root(5, x^4),x,0,1)",
"13. integral ((x - x^5) / sqrt x, x)       @Simplify the integrand first.",
"14. integral (x^(-2/3)+4x^(-1/3), x)",
"15. integral ((7x - 7) / root (3, x), x)",
"16. integral (root (3, x) - 1 / root (3, x), x, 1, 8)",
"17. integral ((x- 1) / x^2, x)       @Break the integrand apart into two fractions.",
"18. integral( (t^6 - t^2)/t^4,t,1,2)       @Simplify the integrand first.",
"19. integral( (x^2+1)/sqrt x,x,1,2)       @Simplify the integrand first.",
"20. integral( (x^3-1)^2, x,0, 2)       @Expand the integrand.",
"21. integral( (x-1)(3x+2),x,1,-1)       @Multiply the integrand out.",
"22. integral( (x-2)(x+1),x)       @Multiply the integrand out.",
"23. integral( (2x-1)(x+3),x)       @Multiply the integrand out.",
"24. integral (1 / (3x)^3, x)",
"25. integral (y^2 root (3, y), y)",
"26. integral( (1+ sqrt x)^2,x)",
"27. integral( (x - 1)^3,x,-1,1)",
"28. integral ((x+2)^4, x)",
"29. integral ((x^2 - 4) / (x+2), x)",
"30. integral ((t^2 - 1) / (t+1), t)",
"31. integral ((t^3 - 1) / (t - 1), t)",
"32. integral ((t^4 - 1) / (t^2+1), t)",
"33. integral (cos x, x)",
"34. integral (sin x, x)",
"35. integral( 1+cos t,t, 0,x)",
"36. integral (x - cos x+1, x)",
"37. integral (sin x cos x, x, -pi, pi)",
"38. integral (1 / sin^2 x, x)",
"39. integral (csc^2 theta, theta)",
"40. integral ((sec x) / cos x, x)",
"41. integral (tan^2 theta+1, theta)",
"42. integral (csc x cot x, x)",
"43. integral( sec x tan x, x,0, pi/3)",
"44. integral (sec^2 x - sec x tan x, x)",
"45. integral ((sec^3 x+tan x) / sec x, x)       @Simplify the integrand first.",
"46. integral (abs x, x, -1, 1)       @Many textbooks would break up the interval of integration to get"
  " rid of the absolute value, but this is actually not necessary,"
  " because $abs(x)$ can be integrated directly.",
"47. integral (x abs x, x, -1, 1)",
"48. integral (1+abs x,  x, -1, 1)",
"49. integral (abs (x - 1) abs (x+1), x, -2, 2)       @Break up the interval of integration.",
"50. integral( abs(x-x^2),x,-1,2)       @Break up the interval of integration.",
"51. integral( u(sqrt u + root(3, u)),u,0,1)       @Multiply the integrand out.",
"52. integral( abs(x^2-1),x,-2,3)       @Break up the interval of integration.",
"53. integral( abs(x-x^2),x,-1,2)       @Break up the interval of integration",
"54. integral (abs (sin x), x, -pi/2, 0)       @Break up the interval of integration.",
""};

/*  6.17.13,  problems read from intfund.mhw */
char *problems151[] = {
"1. diff (integral(2,t,-2,x),x)",
"2. diff (integral(sqrt (1 - t),t, 0,x),x)",
"3. diff (integral(t^(11/5),t, x,0),x)",
"4. diff (integral(sqrt(t^5+1),t,1,x),x)",
"5. diff (integral((1 - sqrt t) / sqrt t, t,1,x),x)",
"6. diff (integral((2 - sqrt(t))^9,t,x,0),x)",
"7. diff (integral(t / sqrt (1 - t^3), t,-3,x),x)",
"8. diff (integral(3t^10 (t^3+1)^11,t, x,2),x)",
"9. diff (integral(e^(t^2), t, 0,x),x)",
"10. diff (integral(t ln t,t, e,x),x)",
"11. diff (integral(1 - cos t, t, 3, x),x)",
"12. diff (integral(sin (t^3),t, 0,x),x)",
"13. diff (integral(sin(t^7),t,0,x),x)",
"14. diff (integral(1 - t^3, t, x,cos x),x)",
"15. diff (integral(abs (t^2 - 4),t, 4,x),x)",
"16. diff (integral(csc t tan^3 t,t,1,-x),x)",
"17. diff (integral(root (3,1+t+t^2), t,2,1+x),x)",
"18. diff (integral((1+t^2)^(1/5), t,1,5x),x)",
"19. diff (integral(10,t,-2,x^3),x)",
"20. diff (integral(t^2+t+1, t,-1,x^2),x)",
"21. diff (integral(t^2/(t^2+1),t,1,sqrt x),x)",
"22. diff (integral(sqrt (1+t^2),t,0,x^3),x)",
"23. diff (integral((t^2+3)^18, t,10,1+x+x^2),x)",
"24. diff (integral((1+t^2)^3/4, t,1,x^6),x)",
"25. diff (integral(sqrt (t+sqrt t), t, a,x^4),x)",
"26. diff (integral(csc t, t, pi/2,x^3),x)",
"27. diff(integral(x^99,x),x)",
"28. diff (integral((sin t)/t,t,x^3, 2pi),x)",
"29. diff (integral(sin^3 (t^2), t, 0,sqrt x),x)",
"30. diff (integral(abs (t+sqrt t), t, 4,4x^2),x)",
"31. diff (integral((2t - 1) / (t^2+2t+1), t,1,x sin x),x)",
"32. diff (integral((t^10 - 1) / (t^2+1),t,1,cos x),x)",
"33. diff (integral(t^2+t+1, t,1,sec x),x)",
"34. diff (integral(t cos t, t, pi,tan x),x)",
"35. diff (integral(t cos t^2, t, 5, tan x),x)",
"36. diff (integral((1 - t^2)^2, t,1+x,1+x^2),x)",
"37. diff (integral(1/t, t,3x,5x),x)",
"38. diff (integral(1/t, t,sin x,x^2),x)",
"39. diff (integral(1 /(1+t^2), t,-x,3x^2+1),x)",
"40. diff (integral((t^2+1)^7, t,x,x^2),x)",
"41. diff (integral(sqrt (t^4+2), t, -x,x),x)",
"42. diff (integral(1 / sqrt (1 - t^2), t, x ,x^2),x)",
"43. diff (integral(tan t, t,sin x,x),x)",
"44. diff (integral(sin t, t, -x, 1-x^2),x)",
"45. diff (integral(tan^3 t, t,-x,-x^2),x)",
"46. diff (integral(t^2 cos (t^3), t,2x,4x),x)",
"47. diff (integral(sin(t^2),t,root(5,x), -x),x)",
"48. diff (integral(1 - t^2, t,cos x,sin x),x)",
"49. diff (integral(1 /(1 - t^5), t,-x^2,x^2),x)",
"50. diff (integral(sqrt (1 - t^2),t, 0,1),x)",
"51. diff(integral(e^x^2 sin x,x),x)",
""};

/*  6.17.13,  problems read from intsubst.mhw */
char *problems152[] = {
"1. integral (3t/(t^2+1)^2, t )",
"2. integral( 1/(3x-1)^2,x)",
"3. integral ( (1 - y)^11, y )",
"4. integral (x^3 (1+x^4)^3, x ,0,1 )",
"5. integral ((6 -x)^(-3), x,1,2 )",
"6. integral ((2x+1)^-1/3, x)",
"7. integral (t (3 - t)^(1/3), t, 1, 3 )",
"8. integral (3t (1-3t^2)^10, t )",
"9. integral (y (y+1)^15, y)",
"10. integral ( (y^3+6y^2 - 12y+5) (y^2+4y - 4), y, 0, 1 )",
"11. integral ( t^9 sin (t^10), t)",
"12. integral (x sin(x^2), x,  0, sqrt pi)",
"13. integral ((x^2) /(x^3 +1), x, 1,3)",
"14. integral ( (x+3)/sqrt (x+1), x, 0, 1 )",
"15. integral (x^2 sqrt (x^3+1), x)",
"16. integral (x (x^2+1)^(1/3),x, - sqrt 7, 0)",
"17. integral( x^3(1+x^4)^2,x)",
"18. integral( x(3x^2+1)^(1/2),x)",
"19. integral( 1/(1-t)^8,t)",
"20. integral(x^2 root(3, x^3+1),x)",
"21. integral( sqrt(1+2x),x,0,4)",
"22. integral(2 x/sqrt(1+2x),x,0,4)",
"23. integral (1/(sqrt x (1+ sqrt x)^2), x)",
"24. integral ( sqrt (1+ sqrt x)/ sqrt x , x)",
"25. integral ( 1/ (x + sqrt x), x )",
"26. integral (x^(1/3) cos x^(4/3) ,x)",
"27. integral ( x^2 sqrt (x+3) , x )",
"28. integral ( x sqrt (x-1), x )",
"29. integral ((x+2)/ (x^2+4x+3)^3, x )",
"30. integral ((2 - x^2)/(x^3 - 6x + 1)^5, x )",
"31. integral (sqrt (10 - sqrt x), x, 1, 9 )",
"32. integral ( y^(1/2) (1+y^(3/2))^7, y )",
"33. integral ((1+sqrt x)^4 /sqrt x, x, 1, 4 )",
"34. integral (x^(n-1) sqrt (a+bx^n) , x )",
"35. integral ( (x^2+x) sqrt (2x^3+3x^2+2), x)",
"36. integral( sin 6t,t,0, pi/2)",
"37. integral (sin (3 - 5x), x )",
"38. integral (sec (2x) tan (2x), x )",
"39. integral ( sin(sqrt theta)/sqrt(theta), theta)",
"40. integral ( tan theta sec^3 theta, theta)",
"41. integral (cos (3x)/ sin^3 (3x), x )",
"42. integral (csc^2 (2 theta) cot (2 theta), theta)",
"43. integral (sec^3 theta tan theta, theta )",
"44. integral (sin theta cos theta, theta )",
"45. integral ( x cos (x^2), x)",
"46. integral ((sin (1/x))/ x^2, x)",
"47. integral (cos^4 t sin t, t )",
"48. integral( sec^2 7 theta,theta)",
"49. integral( (tan sqrt x) / sqrt x,x)",
"50. integral( tan^2 x sec^2 x,x )",
"51. integral (sqrt (tan x) sec^2 x, x, 0, pi/4 )",
"52. integral ( (cos x)/ sqrt (2+ sin x), x, 0, 2pi)",
"53. integral (sin (sqrt y)/ sqrt y, y )",
"54. integral (sin^2 x cos x, x )",
"55. integral ( x^(-3) cos (x^(-2)), x )",
"56. integral ((cos x) sqrt (sin x ), x, 0, pi/2)",
"57. integral ((sin (sqrt t) cos (sqrt t))/ sqrt t, t )",
"58. integral ((sin x)/(1+cos x)^4, x, 0, 1)",
"59. integral ( 3 e^x/ (1+3 e^x), x)",
"60. integral (e^(2x) sin (1+ e^(2x)), x )",
"61. integral( sin x root(3, cos x),x)",
""};

/*  6.17.13,  problems read from intpart1.mhw */
char *problems153[] = {
"1. integral( x cos x, x,0, pi)",
"2. integral (x cos (pi x), x, 0,1/2)",
"3. integral( x sin 3x,x)",
"4. integral (theta^2 sin (2 theta), theta, 0,pi/2)",
"5. integral (x^2 cos x, x,0,pi)",
"6. integral (x^3 sin x, x)",
"7. integral (x^3 cos x, x)",
"8. integral (sin (sqrt x) ,x)",
"9. integral (cos (sqrt x), x)",
"10. integral (x sec^2 x, x)",
"11. integral( x csc^2 x,x)",
"12. integral( x sec x tan x,x)",
"13. integral( x sec^2 x,x)",
"14. integral (x^3 cos (x^2), x)",
"15. integral( (x+1) e^x,x)",
"16. integral (x e^(-2x), x)",
"17. integral (x e^(1-5x), x)",
"18. integral (x^4 e^x, x)",
"19. integral ((1+3x+x^2) e^x, x)",
"20. integral (x^2 e^(2x), x)",
"21. integral( x^3 e^(x^2),x)",
"22. integral (x^5 e^x, x)",
"23. integral (x^3 3^x, x)",
"24. integral (t^2 4^t, t)",
"25. integral (e^(sqrt x), x)",
"26. integral (e^(root(3, x)), x)",
"27. integral (e^(sqrt (3s+9)), s)",
"28. integral (ln (1+4x), x)",
"29. integral (ln (x)/x^2, x)",
"30. integral (x^(3/2) ln x, x, 1,4)",
"31. integral (x^3 ln x, x)",
"32. integral (x^2 ln (x^3), x)",
"33. integral( t^2 ln t,t)",
"34. integral (ln (1+x^2)/x^2, x)",
"35. integral ((ln (x))^3, x)",
"36. integral ((ln (x))/(x+9)^2, x)",
"37. integral (x ln (4+x^2), x, 0,1)",
"38. integral (x (ln x)^2, x)",
"39. integral (ln (x+x^2), x)",
"40. integral ((ln (x+1))/ sqrt(x+1), x)",
"41. integral (sqrt x ln (x^3), x)",
"42. integral (sqrt x ln x, x)",
"43. integral (e^x ln (1+e^x), x)",
"44. integral (sin (ln x), x)",
"45. integral (cos (ln x), x)",
"46. integral( cos(4 ln x),x)",
"47. integral( cos x ln (sin x),x)",
"48. integral (e^x sin(x/2), x)",
"49. integral (e^(2x) (3-sin (4x)), x)",
"50. integral (e^(2x) cos (pi x), x, 0, 1)",
"51. integral ((sin x)/e^x, x)",
""};

/*  6.17.13,  problems read from intrev.mhw */
char *problems154[] = {
"1. integral (x (2x+3)^99, x)",
"2. integral ((x^3 -1)/(x^2+1), x)",
"3. integral ((2x +1)/((x^2+1)(x+3)), x)",
"4. integral (x^2/sqrt (1-x), x)",
"5. integral (x^3 sqrt (1-x^2), x)",
"6. integral (x^7/(1+x^4)^(3/2), x)",
"7. integral( xe^(2x),x)       @better done by substitution",
"8. integral( x^2 e^(-x), x,0,1)       @Usually in a product of a polynomial and transcendental, you"
  "  differentiate the polynomial and integrate the transcendental if you can.",
"9. integral( t e^(-t),t,0,1)",
"10. integral( x 5^x,x)",
"11. integral( (2x+3) e^x,x)",
"12. integral (x^2e^(-x^3), x)",
"13. integral( x^3 e^(x^2),x)       @First perform a substitution.",
"14. integral( x^5 e^(x^2),x)",
"15. integral( e^(sqrt x),x)       @First perform a substitution.",
"16. integral( t^3 e^t,t)",
"17. integral( x ln x,x)       @Differentiate the logarithm, because its derivative"
  " is a rational function.",
"18. integral( (ln x)^2,x)       @If any factor is a logarithm or a power of a logarithm,"
  " choose that for the part to differentiate.",
"19. integral( t^2 ln t,t)",
"20. integral( (sqrt t) ln t, t,1,4)",
"21. integral( ln(sqrt x),x)",
"22. integral ((ln x)/x, x)",
"23. integral (1/(x ln x), x)",
"24. integral( x cos x,x)",
"25. integral( x sin 4x,x)",
"26. integral( x cos 2x, x,0, pi/2)",
"27. integral( sin(3x) cos(5x),x)       @Better done by using a trig identity first.",
"28. integral( sin(2x) sin(4x),x)       @Better done by using a trig identity first.",
"29. integral (sin^2 theta, theta)",
"30. integral (cos (x) sin^2 (x), x)",
"31. integral (sin^5 (2u), u)",
"32. integral (sec^5 x, x)",
"33. integral( theta sin theta cos theta,theta)",
"34. integral( theta sec^2 theta,theta)",
"35. integral( x csc^2 x, x,pi/4, pi/2)",
"36. integral( x^2 cos 3x,x)",
"37. integral( x^2 sin 2x,x)",
"38. integral (x sin (x^2), x)",
"39. integral( x^5 cos(x^3),x)",
"40. integral( sin(sqrt x),x)",
"41. integral( arccos x, x,0, 1/2)",
"42. integral( arcsin x,x)",
"43. integral( arctan x, x)       @The derivative of arctan is a rational function.",
"44. integral( x arctan x,x)       @Usually when one factor is a polynomial and"
  " the other is transcendental, we differentiate the"
  " polynomial.  But the derivative of arctan is a"
  " rational function, so if you differentiate the"
  " arctan, the transformed integrand will be a rational"
  " function.",
"45. integral( e^(2 theta) sin(3 theta),theta)",
"46. integral( e^(-theta) cos(3 theta),theta)",
"47. integral(  cos(ln x)/x,x)",
"48. integral( cos x ln(sin x),x)",
"49. integral( sin(ln x),x)       @Note this is not a product of sin and ln, but"
  " a composition of functions.  First perform a substitution.",
"50. integral( cos(ln x),x)",
"51. integral(abs(sin x),x,0,3pi/2)",
"52. integral(abs(sin x),x,0,5pi/2)",
""};

/*  6.17.13,  problems read from limexp.mhw */
char *problems155[] = {
"1. lim(x->infinity, 2^x)",
"2. lim(x->infinity,pi^(-x))",
"3. lim(x-> - infinity, (sqrt 2)^x)",
"4. lim(x->infinity,5^(2x+5))",
"5. lim(x-> infinity, 2 ^(- 8 x))",
"6. lim(x-> - infinity, 3^(- x^2))",
"7. lim(x-> - infinity, e^(5x^3))",
"8. lim(x-> 1/2, e^(5x^3))",
"9. lim(x-> infinity, e^( sqrt x))",
"10. lim(x-> 0+, e^( -1/sqrt x))",
"11. lim(x-> 0+, e^(- 1/x))",
"12. lim(x-> infinity, 1 / (e^x+1))",
"13. lim(x-> 0+, e^(-1/x)+1/e^x)",
"14. lim(x-> infinity, e^(1 / x)+1 / e^x)",
"15. lim(x-> - infinity, e^(1/x)+1/e^x)",
"16. lim(x-> - infinity, 1/x - e^(- x^4))",
"17. lim(x-> infinity, sqrt (e^(-x)))",
"18. lim(x-> 0, sqrt (1+e^(2x)))",
"19. lim(x-> pi -, e^( cot x))",
"20. lim(x-> - infinity, sqrt (1+e^(2x)))",
"21. lim(x-> infinity, sqrt (1+ e^(2x)))",
"22. lim(x-> infinity, root(4, 16+ e^(-x)))",
"23. lim(x-> infinity, e^(e^(-x)))",
"24. lim(x-> infinity, ln (1/x +(e^(1/x))))",
"25. lim(x-> pi-, e^(cot^2 x))",
"26. lim(x-> pi+, e^(cot x))",
"27. lim(x-> pi, e^( sin 3x))",
"28. lim(x-> pi+, 2^(sin x))",
"29. lim(x-> pi/2-, e^(tan x))",
"30. lim(x-> 0, (pi)^(sin x))",
"31. lim(x-> 0, cos (pi/4e^(-x)))",
"32. lim(x-> infinity, sin^2 (e^(-x)))",
"33. lim(n-> infinity,(1+1/n)^n)",
"34. lim(n-> infinity,(1+1/(n+1))^n)",
"35. lim(n->-infinity,(1+1/n)^n)",
"36. lim (x-> infinity, (1 - 1/x)^x)",
"37. lim (x-> infinity, (1+3/x)^(-x))",
"38. lim (x-> infinity, (1+1 / (2x))^x)",
"39. lim (x-> infinity, (1-2/x)^(-x+3))",
"40. lim (x-> infinity, (1+1/x^2)^x)",
"41. lim (x-> infinity, (1 - 1/x^2)^(x^2-1))",
"42. lim (x-> infinity, (1+1 /(x^2-2x))^x)",
"43. lim (x-> - infinity, (1+1/x)^(x^2))",
"44. lim (x-> infinity, (1+1 / (pi x))^(3x))",
"45. lim (x-> - infinity, (1+1/x)^(x^2))",
"46. lim (x-> infinity, (1+1 / x^10)^x)",
"47. lim (x-> infinity, (1+1 / (sqrt(2 x)))^(sqrt(2x)))",
"48. lim(h->-infinity, e^(-h) ln(e^h+1))",
"49. lim (x-> 0-, (1+ sin x)^(csc x))",
""};

/*  6.17.13,  problems read from lhopital.mhw */
char *problems156[] = {
"1. lim(x->0, sin(x)/x)",
"2. lim(x->0, tan(x)/x)",
"3. lim(x->0, (1-cos x)/x)",
"4. lim(x->0, (1-cos x)/x^2)",
"5. lim(x->0, (e^x-1)/x)",
"6. lim(x->0, ln(1+x)/x)",
"7. lim(x->0, (sin 5x)/(sin 3x))",
"8. lim(x->0, (sin^2 x)/x)",
"9. lim(x-> infinity, (x^2) / ln x)",
"10. lim(x->1, (sin (x pi)) / (x - 1))",
"11. lim(x->0, (1 - cos x) / x^2)",
"12. lim(x->0,(e^(2x) - 1)/(sin x))",
"13. lim(x->0, (3^x - 1) / (5^x - 1))",
"14. lim(x->0, (ln^2 (1+x)) / x)",
"15. lim(x->infinity, (3^x) / 5^x)",
"16. lim(x->0, (e^(4x) - 1) / (2x))",
"17. lim(x->0+, (x^(-1/2)) / ln x)",
"18. lim(x->0+,(ln x)/sqrt x)",
"19. lim(x->infinity, (ln (ln x)) / ln x)",
"20. lim(x->0, (ln (cos x)) / sin x)",
"21. lim(x-> e-, (1 - ln x) / (x - e)^2)",
"22. lim(x->infinity, (ln (x^2+10)) / ln x)",
"23. lim(x->1-, (ln x) / arccos x)",
"24. lim(x->2,(root(3, x) - root(3, 2))/(x-2))",
"25. lim(x->3, (sqrt (x+1) - 2) / (x^2 - 9))",
"26. lim(x->0,(e^x-1)/sin x)",
"27. lim(x->0, (1 - e^(3x)) / sin(3x))",
"28. lim(x->infinity, (x^10) / e^x)",
"29. lim(x->2, ( sin (4 - 2x)) / (x^3 - 8))",
"30. lim(x->infinity, (x^(3/2)+5x - 4) / (x ln x))",
"31. lim(x->infinity,(ln ln x)/sqrt x)",
"32. lim(x->0, x/(arcsin 5x))",
"33. lim(x->0, (arctan x - x) / x^2)",
"34. lim(x->0, (sinh (x^2) - tanh (x^2)) / x^3)",
"35. lim(x-> pi/2,(cos x)/(x - pi/2))",
"36. lim(x->0, ( sqrt (1+x) - sqrt (1 - x)) / x)",
"37. lim(x->infinity, 6 (x - sqrt (x^2+x)))",
"38. lim(x->- infinity, x+sqrt (x^2+1))",
"39. lim(x->1,1/(ln x) - 1/(x-1))",
"40. lim(x->pi/2+, ((pi/2) - x) tan x)",
"41. lim(x->0+, (sin x) ln (sin x))",
"42. lim(x->-infinity,xe^x)",
"43. lim(x->infinity, x e^(-x))",
"44. lim(x->0+, x^3 ln x)",
"45. lim(x->infinity,x^3e^(-x^3))",
"46. lim(x->1+, (ln x) tan (pi x/2))",
"47. lim(x->infinity, x^(1/x))",
"48. lim(x->0+, x^(1/ln x))",
"49. lim(x->1/2-, (1 - 2x)^ln (2x))",
"50. lim(x->0+, x^(sin (x^2)))",
"51. lim(x->infinity, (1+x^(-2))^x)",
"52. lim(x->infinity, (x^3+1)^(1/ln x))",
"53. lim(x->infinity,(1+3/x)^(5x))",
"54. lim(x->infinity,((2x-1)/(2x+1))^(x+1))",
"55. lim(x->infinity,(x/(x - 1))^x)",
"56. lim(x->0+,x^(2sin x))",
"57. lim(x->0+,(-ln x)^x)",
"58. lim(x->infinity, (e^x+1)^(1/x))",
"59. lim(x->pi/2, abs (sec x)^(cos x))",
"60. lim(x->infinity, (cosh x)^(1/x^2))",
"61. lim(x->infinity,x(ln(x+5)-ln x))",
"62. lim(x->0+, (e^(-1/x)) / x)",
"63. lim(x->0+, (sin x) e^ (1/x))",
"64. lim(x->0+, (ln (1/x))^(x^2))",
"65. lim(x->(pi/2)-,(tan x)^( cos x))",
"66. lim(x->0+, (cot x)^sin x)",
"67. lim(x-> infinity, (e^(2x) - x^2) / (e^(2x) + x^2))",
"68. lim(t->2, sin (t^2 - 4) / (t - 2))",
"69. lim(t-> 0, sin^2 (t/2) / sin (2t))",
""};

/*  6.17.13,  problems read from leadterm.mhw */
char *problems157[] = {
"1. lim(x->infinity, (3x+1)/(2x-6))",
"2. lim(x->infinity, (x^2-2x+3)/(3x^2+x))",
"3. lim(x->infinity, (x^3+x^2-x-3)/(x^3+x+1))",
"4. lim(x->infinity, (3-x)/(x^2-2x-8))",
"5. lim(t->-infinity,(6t^2 + 5t)/((1-t)(2t-3)))",
"6. lim(x-> infinity, x / (x^2 - 1))",
"7. lim(x-> infinity, (5x + 10) / (x (x+3)))",
"8. lim(x-> infinity, (x^2 - x) / (x^3-x^2))",
"9. lim(x-> infinity, x^3/(x + 5) - x^2)",
"10. lim(x->infinity, (x^3+x+1)/(x^4+x^2+1))",
"11. lim(x->infinity, (x^4+x^2+1)/(x^5-x^3+x))",
"12. lim(x->infinity, (x^7-1)/(x^6+1))",
"13. lim(x->infinity, (5x^3+4x)/(2x^3-x^2+1))",
"14. lim(x->infinity, (11-x^5)/(x^2+x+1))",
"15. lim(x->infinity, (5x^3+5x+1)/((1-x)(2x-3)))",
"16. lim(x->infinity, ((1-x)(2+x))/((1+3x)(2-3x)))",
"17. lim(x-> infinity, (9x^3 - x) / (x^3 +1))",
"18. lim(x-> infinity, (x-2) / (x-3) + (x^3+2) / (x^3-3))",
"19. lim(x-> infinity, (x^2+1) / x^4)",
"20. lim(x-> infinity, x^2/(x^3+1) + x^2/(x^3 - 1))",
"21. lim(t-> infinity, t / (t^(1/2) - 2t^(-1/2)))",
"22. lim(x-> infinity, (x + sqrt x) /(x- sqrt x))",
"23. lim(x-> -infinity, sqrt(3x^4-x)/(x^2-10))",
"24. lim(x-> infinity, sqrt(x^2+4x)/(4x+1))",
"25. lim(x-> infinity, sqrt(x^2 - 1)/sqrt(x^2+1))",
"26. lim(x-> infinity,sqrt(x^2+5x)/(1- x))",
"27. lim(x->infinity,sqrt((2x^2-1)/(x+8x^2)))",
"28. lim(x->infinity, sqrt(1+4x^2)/(4+x))",
"29. lim(x->-infinity,sqrt(x^2+4x)/(4x+1))",
"30. lim(x->-infinity, sqrt(x^2+x+1) + x)",
"31. lim(x-> infinity, 8x/ sqrt (4x^2-1))",
"32. lim(x-> infinity, (sqrt x) / (4 sqrt x + x))",
"33. lim(x-> infinity,sqrt(1+x)/sqrt(x-1))",
"34. lim(x-> infinity, sqrt(x^2+x -1) /(x-1))",
"35. lim(x-> infinity, sqrt (x^2/(1+3x^2)))",
"36. lim(x-> infinity, sqrt(4 + x^2)/(1+4x))",
"37. lim(x-> infinity, sqrt (1+x^2) / (x-1))",
"38. lim(x-> infinity, 2x / sqrt (4x^2 - 1))",
"39. lim(x-> infinity,sqrt((x^2-1)/(x+7x^2)))",
"40. lim(x-> -infinity, x / sqrt (4x^2+5))",
"41. lim(x-> -infinity, sqrt ((1 - x) / (3 - x)))",
"42. lim(x-> -infinity,root(3, x+1) / root(3, x - 1))",
"43. lim(x->infinity,root(3, 1+x)/root(3,x))",
"44. lim(x-> infinity, root(3, x^2+6)/(x+1))",
"45. lim(x-> -infinity, root(3, x^3+8)/(x - 1))",
"46. lim(x-> -infinity, (8+x^2) / (x (x - 1))^(1/3))",
"47. lim(x-> infinity, (x^2+x+1)^(5/3) / (x-1)^4)",
"48. lim(x-> infinity, x sqrt (9x^2 +1) / sqrt (3x^3 +1))",
"49. lim(x-> infinity, (16 - x^2)^(1/3) / (4 - x))",
"50. lim(x-> infinity, (2x^(2/3)-x^(1/3)+1)/(x^(1/3)-1)^2)",
"51. lim(x-> infinity, x/sqrt(x^2+1) + 2x/sqrt(x^2-1))",
"52. lim(x-> infinity, root(3, x^4+1)/(x+1) + root(3, x^4-1)/(x-1))",
""};

/*  6.17.13,  problems read from limrev.mhw */
char *problems158[] = {
"1. lim(x->-1, (1+3x - x^2) / (x^2+x+3))",
"2. lim(x->0, (x^2 - 5x) / (x^2 - 2x))",
"3. lim(x->infinity, (x^2(1 - 5x)) / (5x^3+x+1))",
"4. lim(x->-3-, (3 abs x +9) / (x^2 - 9))",
"5. lim(x->infinity, x^2 / (x+2) - x^3 / (x^2+2))",
"6. lim(x->- infinity, x^2 / (1+x)+x^2 / (1 - x))",
"7. lim(x->infinity, ((3x^2+1) / (10+3x^2))^x^2)",
"8. lim(x->0-, sqrt (9+ sqrt(-x)))",
"9. lim(x->5/2-, x^2 - sqrt(5 - 2x))",
"10. lim(x->3-, 1 / (5 - sqrt (x^2+16)))",
"11. lim(h->0, (sqrt (x+h) - sqrt x) / h)",
"12. lim(x->infinity, sqrt x - sqrt(x^2 - x - 1))",
"13. lim(x->infinity, (x - 10) / sqrt(x^2+100))",
"14. lim(t->81, (t^(3/4) - 27) / (t^(1/2) - 9))",
"15. lim(x->-1, (4 - root(3, (x^2 - 6x+1)^2)) / (2 - root(3, (x^2 - 6x+1))))",
"16. lim(x->0+, (1-x)^(4/x))",
"17. lim(x->0+, (1+sqrt x)^(1/x))",
"18. lim(x->-infinity,arctan(x^3))",
"19. lim(x->0-, (sin x) / abs x)",
"20. lim(x->infinity, sqrt x sin (1/x))",
"21. lim(x->0, (cos x - 1) / (2x))",
"22. lim(x->pi, (1+cos x ) / (x - pi)^2)",
"23. lim(x->0, (1 - cos 3x) / (5x^2))",
"24. lim(x->0,(sin x^2) / (x^4 - 3x^2))",
"25. lim(x->infinity, (sin 3x+x) / (2x+3))",
"26. lim(x->1, (cos (pi x / 2)) / (x - 1))",
"27. lim(x->0, (x^2 - 5x) / sin (3x))",
"28. lim(x->0, (cos^2 x - sin^2 x) / x)",
"29. lim(x->1+, (sin (pi x)) / abs (x - 1))",
"30. lim(x->0, 1/x^2 - 1 / (1 - cos x))",
"31. lim(x->0+, arctan (1 / x))",
"32. lim(x->0, (arcsin (5x)) / (11 x))",
"33. lim(x->pi-, arcsin (cos x))",
"34. lim(x->0+,(sin x)(ln x)^3)",
"35. lim(x->0+,ln(tan x))",
"36. lim(x->0,csc x ln (1 - x))",
"37. lim(x->0+, (e^(1/x) - 1) tan x)",
"38. lim(t->0, (1 - e^(sin t)) / (1 - e^t))",
"39. lim(x->- infinity, (1 - e^x) / (1+e^x))",
"40. lim(x->infinity, x e^(-(x^(1/10))))",
"41. lim(x->infinity, ln(ln x)/ln x)",
"42. lim(x->0-, 5^(ln (abs x)))",
"43. lim(x->0+, e^(root (3, ln (sqrt x))))",
"44. lim(t->0, (sinh (5t)) / t)",
"45. lim(x->0, (sin^5x)/sin(x^5))",
"46. lim(x->0+, ln (1 - ln (2x)))",
"47. lim(x->1+, (x^2 - 1) ln (x - 1))",
"48. lim(x->infinity, (1+5/x)^(x/10))",
"49. lim(x->0+, (e^x) / ln x)",
"50. lim(x->0+,(1 - e^(-x)) x^(-1/2))",
"51. lim(x->1+, (ln x)^ln x)",
"52. lim(x->-infinity,e^(x/2) cos x)",
"53. lim(x->1+,(ln x)^sin x)       @The two-sided limit is undefined, because"
  " the function isn't defined when $ln x$ is"
  " negative and $sin x$ is irrational."
"54. lim(x->0+,(root(3, x)-1)/(root(4, x)-1))",
"55. lim(x->0,(e^(ax)-e^(bx))/x)",
""};

/*  6.17.13,  problems read from difdef2.mhw */
char *problems159[] = {
"1. ln x",
"2. e^x",
"3. 2^x",
"4. a^x",
"5. sinh x",
"6. cosh x",
"7. e^(-x)",
"8. e^(x+3)",
"9. x e^x",
"10. ln (abs x)",
"11. (1/x) e^x",
"12. (x^2+3) e^x",
"13. (3x^3) e^(2x)",
""};

/*  6.17.13,  problems read from difexp.mhw */
char *problems160[] = {
"1. e^(2x+3)",
"2. e^(3 - x^3)",
"3. e^(3 - x - x^3)",
"4. e^(-1/x)",
"5. 3 - e^(-(x^2)/2)",
"6. xe^(x^2)",
"7. x^2 e^(-x^3)",
"8. e^(sqrt x+1)",
"9. e^ sqrt(x+1)",
"10. e^sqrt x +1",
"11. e^sqrt x + sqrt (e^x)",
"12. root(3, x^3+e^(3x))",
"13. (e^(x^2)+x)^2",
"14. (x^2+x+1) e^(2x)",
"15. 1 / (e^x+e^(-x))",
"16. e^(e^x)",
"17. e^(x+e^x)",
"18. (e^x - e^(-x))/(e^x+e^(-x))",
"19. e^(x - e^x^2)",
"20. e^(sin (3x))",
"21. e^(sin^2 x)",
"22. e^(sin x +cos x)",
"23. e^cos (2x)",
"24. cos (2e^x)",
"25. cos (e^(2x))",
"26. sin (e^(7x))",
"27. sin (2e^x)",
"28. (cos x )e^(-2x)",
"29. cos (e^(-x^2))",
"30. tan (e^x)",
"31. cos (1 - e^(-x))",
"32. sin (x - e^(-x))",
"33. x^2 e^(x^2) sin (x^2)",
"34. e^arcsin x",
"35. e^arccos (x^2)",
"36. arctan (e^x)",
"37. 5^x",
"38. 4^(-x+x^2)",
"39. 10^(-sqrt x)",
"40. 5^ sqrt(1+x)",
"41. 2^(x^2)",
"42. x 3^(x^2)",
"43. 2^x e^(5x)",
"44. 1 / x 2^ln x",
"45. 3^(6^x)",
"46. 2^(cos x) sin x",
"47. 2^(3^cot x)",
""};