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ELF	>`�@@1. 8^x = 2^(x^2)2. 4^(x+2) = 2^(x - 1)3. 2^(6x) = 64^(x^2)4. 3^(2x) = 9^(3x-2)5. 4^(x^2) = 256^(x-1)6. 10^x - 1= 997. 8^(3x - 2) = 648. 4^x = 8^(x+3)9. 8^(x - 1) = 4^(x^2)10. 5^(x^2-x) = 2511. (4/5)^(x^3) = 64/12512. (2/3)^x = 27/813. (sqrt 2)^x = 814. 2^(x^2) = (1/4)^x15. 10^(3x-1) = 9216. e^(2x+1) = 40517. 3^x = 1818. 3^(x/2) = 619. 11^x = 2220. 2^x = 1021. 2^(-x) = 1/522. e^(x/2) = 1023. 2^(3^x) = 524. 2^(x/3) = 3^(x/2)25. 3^(- x^2) = 426. 3^(- x^2) = - 527. 2^(2x - 2) = 6^(- x)28. 5^(5 - 2x) = 2629. 2^x = 3^x30. 2^x 3^x = 931. 2^x = 3^(2x - 1)32. e^(2 ln x) = 433. e^( - ln x) = 234. 2^x / (2^x - 1) = 535. x^sqrt 3 = 836. x^sqrt 2 = 837. 10^(2x) = 3(10^x)38. e^(4x) = 5e^(2x)39. 1/2 e^x = e^(2x - 1)40. 2^x - 6 (2^-x) = 641. e^(6x) - 6e^(3x) + 5 = 042. e^(2x) - e^(-2x) = 243. e^x + e^(-x) - 1 = 044. e^x - e^(-x) = 3(e^x + e^(-x))45. x^2 e^(2x)+2 x e^(2x) = 8 e^(2x)46. 4^x - 6 (2^x) = -847. 5^x+3 = 10 (5^-x)48. 2 e^(2x) - 9 e^x+4 = 049. (2^x - 1) / (2^x+1) = 2^x50. e^(3x) - 2e^(2x) + 4e^x - 8 = 051. 2e^(3x) + 6e^(2x) - 3e^x - 9 = 052. 6e^(-3x) + 9e^(-2x) - 8e^(-x) - 12 = 053. 5e^(2x) - 7e^x + 14 + 12e^(-x) = 054. 4e^(2x) - 4e^x + 13 - 12e^(-x) + 3e^(-2x) = 01. i2. 1 - sqrt 33. -i4. -105. 4i6. -4i7. -5i8. 5i9. 1 + i10. 1 -i11. -1 + i12. -1 -i13. 3 - (sqrt 3)i14. -20i15. 5 - 6i16. 2 + 2i17. 1 - (sqrt 3) i18. sqrt 3 - i19. -sqrt 3 + i20. -1 + (sqrt 3) i21. -1 - (sqrt 3) i22. 1 + sqrt(3) i23. sqrt 3 + i24. -sqrt 3 -i25. sqrt 5 - (sqrt 11)i26. - sqrt 7 - 3i27. 4+4(sqrt 3)i28. 2 sqrt 3 - 2i29. sqrt 5 + 4i30. 4sqrt 2 - 4i sqrt 231. 1/i32. 1/(1+i)33. 4 / (-3 + 3i)34. (2 - 2i) / (-1 - i)35. 1/(1+sqrt(3) i)36. 7i (-5i)37. 4i (2 - i)38. (- 3i) (2+i)39. (1+i) (-2 - 2i)40. (3+3i) (1 + i)41. (sqrt 3+i) (- sqrt 3 - i)42. (3-3i)/ (1 + i)43. (1 - i)^244. (1+i)^245. (1+i)^346. (1+i)^447. (sqrt 2 - i)^1048. (-sqrt 2 - i sqrt 2)^749. 2(cos pi - i sin pi)50. -3(cos(pi/6) - i sin (pi/6))1. ( cos (deg (15)) + i sin (deg (15)))^82. (cos (deg (5)) + i sin (deg (5)))^123. ((sqrt 2) (cos (5pi/4) + i sin (5 pi/4)))^64. (cos (pi/5) + i sin (pi/5))^155. (cos (pi/10) + i sin (pi/10))^406. (cos (pi/4) + i sin (pi/4))^107. (1+  (sqrt 3) i)^38. (-(1/2) - (sqrt 3)/2 i )^39. (-sqrt 3 - i)^410. (1 + (sqrt 3)i)^811. (1 + 3i)^712. (1+ (sqrt 3)i)^(-8)13. (- sqrt 3 + (sqrt 3)i)^914. ((sqrt 3) / 2 + 1/2 i)^1015. (2^(1/3) + 2^(1/3) i)^1216. (-1+i)^1817. (1 - i)^10018. ((- sqrt 3) / 2+1/2 i)^10019. ((sqrt 2)/2 - (sqrt 2)/2 i)^2020. 4i (2 - i)21. (sqrt 3 +i) (- sqrt 3 - i)22. ((1 - i) (1+i))^1723. (1+i)^6(sqrt 3 - i)^324. (- sqrt 3 + i)^(-4) (-1-i)^6/((-1+i)^(-2)(- sqrt 3 -i)^3)25. ((2+2i) / (3 - 3i))^526. (cos pi - i sin pi)^527. (-2(cos(pi/6) - i sin (pi/6)))^61. sinh(-x) = - sinh x2. cosh(-x) = cosh x3. cosh x + sinh x = e^x4. cosh x - sinh x = e^(-x)5. sinh(x+y) = sinh x cosh y + cosh x sinh y6. cosh(x+y) = cosh x cosh y + sinh x sinh y7. sinh(x-y) = sinh x cosh y - cosh x sinh y8. cosh(x-y) = cosh x cosh y - sinh x sinh y9. tanh(x+y)=(tanh x + tanh y)/(1+tanh x  tanh y)10. coth(x+y)= (1+coth x coth y)/(coth x + coth y)11. sinh 2x = 2 sinh x cosh x12. cosh 2x = cosh^2 x + sinh^2 x13. tanh 2x = (2 tanh x)/(1+tanh^2 x)14. coth 2x = (1+coth^2 x)/(2 coth x)15. coth^2 x -1= csch^2 x16. 1- tanh^2 x = sech^2 x17. cosh^2 x - sinh^2 x = 118. sinh(ln x)= (x^2-1)/(2x)19. cosh(ln x)= (x^2+1)/(2x)20. coth(ln x)= (x^2+1)/(x^2-1)21. tanh(ln x) = (x^2-1)/(x^2+1)1. tanh(-x)=-tanh x2. coth(-x)=-coth x3. sech(-x)=sech x4. csch(-x)=-csch x5. tanh x coth x =16. tanh(x+y) = (tanh x + tanh y)/(1+tanh x tanh y)7. tanh(x-y)= (tanh x - tanh y)/(1-tanh x  tanh y)8. coth(x-y)= (1-coth x coth y)/(coth x - coth y)9. csch x=(coth x)/ cosh x10. sech x =(tanh x)/ sinh x11. sinh 2x= 2 sinh x cosh x12. sinh^2 x= 1/(coth^2 x -1)13. cosh^2 x= 1/(1-tanh^2 x)14. cosh^2 x= (coth^2 x)/(coth^2 x-1)15. cosh^2 x= (1+csch^2 x)/csch^2 x16. tanh^2 x= (sinh^2 x)/(sinh^2 x+1)17. tanh^2 x= (cosh^2 x -1)/(cosh^2 x)18. tanh^2 x= 1/(csch^2 x+1)19. coth^2 x= (sinh^2 x + 1)/(sinh^2 x)20. coth^2 x= (cosh^2 x)/(cosh^2 x - 1)21. coth^2 x= 1/(1-sech^2 x)22. coth^2 x - 1 = csch^2 x23. sinh^2 x = (tanh^2 x)/(1-tanh^2 x)24. sinh^2 x= (1-sech^2 x)/sech^2 x25. (1+tanh x)/(1-tanh x) = e^(2x)26. sinh x + sinh y = 2 sinh((x+y)/2) cosh((x-y)/2)27. sinh x - sinh y = 2 sinh((x-y)/2) cosh((x+y)/2)28. cosh x + cosh y= 2 cosh((x+y)/2) cosh((x-y)/2)29. cosh x - cosh y= 2 sinh((x+y)/2) sinh((x-y)/2)30. tanh x + tanh y= sinh(x+y)/(cosh x cosh y)31. tanh x - tanh y= sinh(x-y)/(cosh x cosh y)32. (cosh x + sinh x)^2 = cosh(2x) + sinh(2x)33. (cosh x - sinh x)^2 = cosh(2x) - sinh(2x)34. (cosh x + sinh x)^3 = cosh(3x) + sinh(3x)35. (cosh x - sinh x)^3 = cosh(3x) - sinh(3x)36. (cosh x + sinh x)^n = cosh(nx) + sinh(nx)37. (cosh x - sinh x)^n = cosh(nx) - sinh(nx)38. sinh^2 x - sinh^2 y = sinh(x+y) sinh(x-y)39. cosh^2 x - cosh^2 y = sinh(x+y) sinh(x-y)40. sinh^2 x + cosh^2 y = cosh(x+y) cosh(x-y)41. sinh^3 x = (sinh 3x - 3 sinh x)/442. sinh^4 x = (cosh 4x - 4 cosh 2x + 3)/843. sinh^5 x = (sinh 5x -5 sinh 3x + 10 sinh x)/1644. sinh^6 x = (cosh 6x -6 cosh 4x +15 cosh 2x -10)/3245. sinh^7 x = (sinh 7x -7 sinh 5x + 21 sinh 3x - 35 sinh x)/6446. cosh^3 x = (cosh 3x + 3 cosh x)/447. cosh^4 x = (cosh 4x + 4 cosh 2x + 3)/848. cosh^5 x = (cosh 5x +5 cosh 3x + 10 cosh x)/1649. cosh^6 x = (cosh 6x +6 cosh 4x +15 cosh 2x +10)/3250. cosh^7 x = (cosh 7x +7 cosh 5x + 21 cosh 3x + 35 cosh x)/6451. sinh 3x = 3 sinh x + 4 sinh^3 x52. sinh 5x =  5 sinh x + 20 sinh^3 x + 16 sinh^5 x53. sinh 6x = (cosh x) (6 sinh x +32 sinh^3 x +32 sinh^5 x)54. sinh 7x= 7 sinh x + 56 sinh^3 x + 112 sinh^5 x + 64 sinh^7 x55. cosh 2x = 2 cosh^2 x -156. cosh 3x = 4 cosh^3 x - 3 cosh x57. cosh 4x = 8 cosh^4 x  - 8 cosh^2 x + 158. cosh 5x= 16 cosh^5 x -20 cosh^3 x +5 cosh x59. cosh 6x= 32 cosh^6 x - 48 cosh^4 x +18 cosh^2 x -160. cosh 7x= 64 cosh^7 x -112 cosh^5 x + 56 cosh^3 x - 7 cosh x61. sinh^2(x/2) = (cosh x -1)/262. cosh(x/2) = sqrt((cosh x + 1)/2)63. tanh (x/2) = (sinh x)/(1 + cosh x)64. tanh(x/2) = (cosh x - 1)/sinh x65. coth(x/2)= (sinh x)/(cosh x -1)66. coth(x/2)= (cosh x +1)/(sinh x)67. sinh(4x)= 2 sinh(2x) cosh (2x)68. cosh(4x)= cosh^2 (2x) + sinh^2 (2x)69. tanh(4x)= (2 tanh (2x))/(1+tanh^2 (2x))70. coth(4x)= (1+coth^2 (2x))/(2 coth (2x))71. sinh(6x)= 2 sinh(3x) cosh (3x)72. cosh(6x)= cosh^2 (3x) + sinh^2 (3x)73. tanh(6x)= (2 tanh (3x))/(1+tanh^2 (3x))1. sin i2. cos i3. sin ix4. cos ix5. tan i6. sec i7. ln(i)8. ln(-1)9. i^i10. cos i + sin i11. cos i - sin i12. cos i + i sin i13. cos i - i sin i14. cos (ix)+sin(ix)15. cos(ix)-sin(ix)16. cos (ix)+isin(ix)17. cos(ix)-isin(ix)18. sin(ix^2)19. sin (i^3)20. cos (i^5)21. sin (ix)^(-1)22. cos (ix)^323. sin (ix)^(-3)24. sin^(-1) i25. cos^(-1) (ix)26. sin^2 i27. sin^2 (ix)28. -i sin(i ln x)29. 1/i tan(ix)30. i cot(ix)31. -i sin^2(ix^2)32. cos(i ln x)33. 1/i cos^2(ix^3)34. i cot(i ln x)35. sin(x+iy)36. sin(x-iy)37. sin(x+iy)+ sin(x-iy)38. sin(x-iy)+i sin(x-iy)39. cos(x+iy)40. cos(x-iy)41. cos(x+iy)- cos(x-iy)42. cos(x+iy)+i cos(x-iy)43. tan(ix)44. cot(ix)45. tan(i ln x)46. e^(x + iy)47. ln(10i)48. ln(ix)49. ln(sin ix)50. ln(1+sqrt(2)i)1. x^2 + 1 = 02. x^2 + 5 = 03. x^2 + 13 = 04. x^2 + 81 = 05. x^2 + 64 = 06. x^2 + 125 = 07. x^2 + x + 1 = 08. x^2 + 2x + 2 = 09. x^2 + 3x + 3 = 010. 2x^2 + 2x + 1 = 011. 2x^2 + 3x + 2 = 012. 3x^2 + 2x + 1 = 013. 3x^2 + 3x + 2 = 014. -x^2 + x - 2 = 015. x^2 -2x + sqrt 2 = 016. x^2 + 3x  + sqrt 6 = 017. x^2 - 3x + root(3, 15) = 018. -5x^2 + 6x - 8 = 019. 5x^2 - 6x  + 9 = 020. -x^2 + 4x - root (4, 625) = 021. x^2 - 2x + 2 = 022. x^2 - 2x + 5 = 023. x^2 - 4x + 5 = 024. x^2 - 4x + 8 = 025. x^2 - 2x + 10 = 026. x^2 - 4x + 13 = 027. x^2 - 6x + 18 = 028. x^2 + x + 5/4 = 029. x^2 +x + 9/4 = 030. x^2 - 3x + 21/4 = 031. x^2 - ix + 2 =032. x^2 + ix + 2 = 033. x^2 - ix + 3 = 034. x^2 + ix + 3 = 035. x^2 - ix + 6 = 036. x^2 + ix + 6 = 037. x^2 - ix + 12 = 038. x^2 - 3ix + 10 = 039. x^2 +3ix + 10 = 040. x^2 - 7ix + 30 = 041. x^2 +ix +2 = 042. x^2 + ix - 2 = 043. x^2 -i x + 5 = 044. ix^2 + x - i = 045. ix^2 + x + i = 01. x^3 -x + 2 = 01. sum(1,i,1,7)2. sum(1/(i+1),i,1,10)3. sum((3 + i),i,1,3)4. sum(5i + 6,i,1,10)5. sum(i^3, i,2,6)6. sum((i-3)(i+2),i,2,7)7. sum(x^k,k,3,8)8. sum((1-i/10),i,1,10)9. sum(j^2,j,n,n+5)10. sum(i^2-2i+1,i,1,7)11. sum(5i^2-1,i,3,7)12. sum((i/14)^2,i,1,7)13. sum((i^2-5),i,-3,3)14. sum((i^2-3i+1),i,-2,1)15. sum(1/5(i/5)^3,i,1,5)16. sum(i^3,i,1,5)17. sum((i+i^2-i^3),i,1,8)18. sum(i(i-1)(i-2),i,1,8)19. sum(i(i+2),i,1,5)20. sum(4,i,1,20)21. sum(2^(3-i),i,-2,2)22. sum(2^i,i,0,4)23. sum(sqrt i,i,1,5)24. sum( 1 +(-1)^i,i,1,10)25. sum((-1)^i/(i-1),i,2,6)26. sum(3^i,i,0,4)27. sum(2^i/(i+1),i,0,10)28. sum((3/5)^i,i,0,3)29. sum(1/3^(i+1),i,0,4)30. sum((i+1)/20,i,1,9)31. sum(2^i ln i,i,1,4)32. sum((-1)^i cos(i pi/2),i,0,5)33. sum(cos(k pi), k,0,10)34. sum(sin(i pi/3),i,1,5)35. sum(cos(i pi/6),i,1,6)36. sum((-1)^i cos(i pi/2),i,0,5)37. sum( (-1)^(k+1)/k,k,1,n)       @This is called the alternating harmonic sum. There is no simpler formula for it, but for large n, the value approaches ln 2.  Select the whole sum and experiment with evaluating it both to rationals and to a decimal for various values of n.38. sum(i^3+i+1,i,1,n)39. sum(2-5i,i,1,n)40. sum(sqrt k - sqrt(k-1),k,1,n)41. sum((3+2i)^2,i,1,n)42. sum(i(i+1)(i+2),i,1,n)43. sum(k^2(k^2-k+1),k,1,n)44. sum(1/k - 1/(k+1),k,1,n)45. sum(i/n,i,1,n)46. sum(i^2/n^3,i,1,n)47. sum(i(i-1),i,1,n)48. sum(i^3+i+1,i,1,n)49. sum(i^3+2i^2+i+1,i,1,n)50. sum((2+i/n)(2/n),i,1,n)51. sum(i,i,2,n)52. sum(i^2,i,2,n)53. sum(i^3,i,2,n)1. (x+2)^32. (x+2y)^43. (x-3)^44. (x-y)^45. (2a +3b)^46. (x+2)^57. (x-5y)^58. (x+3y)^59. (3x+y)^510. (x-2y)^511. (a^2 + 1)^512. (3a-2b)^513. (x+1/2)^514. (x^2-y)^515. (u/3 -4u)^516. (x+3)^617. (2x+y)^618. (x-3y)^619. (2x-y)^620. (2a-3b)^621. (x-y^3)^622. (x-y)^723. (x-1)^724. (x-y)^725. (-2 +x)^726. (x+y)^827. (3x+y)^928. (x+y)^1029. (3x - 7y)^830. (x^2 +2y)^331. (x^3 -y^3)^832. ((a^2)/b - b^3)^433. (x^2-y^2)^634. (a + a^(-1))^535. (2a^2-b^3)^536. (2/x + x/2)^537. (x/y +y/x)^438. (x^2/y + y^2/x)^639. (x^2 +3x^(-2))^440. (xy +3y^(-2))^841. (a^(-2)- b^(-1))^442. (sqrt x + sqrt y)^543. (1/sqrt x + sqrt x)^644. (sqrt c + sqrt d)^745. (1/sqrt x -2x^2)^746. (a/sqrt x - x/sqrt a)^647. (x+y)^6 - (x-y)^648. (1+a)^7 + (1-a)^749. (1-sqrt 3)^4 + (1+ sqrt 3)^450. (1+sqrt 2)^5 - (1- sqrt 2)^551. (a+b)^8 - (a-b)^852. (a+b)^8 + (a-b)^853. (x-2+y)^354. ((1+h)^3 -1)/h55. ((x+h)^6 - x^6)/h56. (2(x+h)^5 -2x^5)/h1. x^2 = i2. x^2 = -13. x^2 = -i4. x^2 = -165. x^2 = -2i6. x^2 = 16i7. x^2 = 4 - 4i sqrt 38. x^3 = -19. x^6 = -110. x^3 = i11. x^4 = i12. x^4 = -8113. x^3 = - 6414. x^3 = 6415. x^3 = 64 i16. x^3 = - 64 i17. x^5 = - 24318. x^4 = -1 - (sqrt 3)i19. x^4 = -1+(sqrt 3)i20. x^3 = -sqrt(3)/2 - i/221. x^3 = 8 - 8 (sqrt 3)i22. x^4 = -8+8(sqrt 3)i23. x^2 = 3 + 4i24. x^2 = 1+2i25. ix^2 + x - 3 = 026. x^2 + x - i = 027. x^2 - x + 1- i = 028. ix^2 - 2ix +1 = 029. ix^2 - (2-i)x +1- i = 030. ix^2 - 3ix + 1 -i = 01. lim(x-> 5, sqrt(5))2. lim(x-> -3, x )3. lim(x-> 5, -2x+15)4. lim(x-> 1/3, 3x-1)5. lim(x-> -3, x^2)6. lim(x-> 5, -2x^2)7. lim(h-> 0, 2h+h^2)8. lim(x-> 1, x^2-2x+1)9. lim(t-> 0, 2 - 4t+t^2)10. lim(x-> -2, x^2-2x-10)11. lim(x-> 3, 5x^2+2x-1)12. lim(x-> -3, 3x^2-x-15)13. lim(x-> 1/4, (3x-1)(x-4))14. lim(x-> 1/2, (x-1)(x+4))15. lim(x-> 6, 8(x-5)(x+5))16. lim(x-> - 3, x^3+21)17. lim(x-> -2, x^3 - 2x^2+4x+8)18. lim(x-> -1, x^3+x^2+7)19. lim(x-> - 1, 3x^2(x-1))20. lim(x-> sqrt 2, (x^2+2)(x-2))21. lim(x-> - 1/3, x^2(6x-1))22. lim(x->2, (x^2-1)(x^2+x))23. lim(x->3, (x^2-x)(x^2+x))24. lim(u-> -2, 3u-u^5)25. lim(u-> -1, u^3-u^5)26. lim(u-> sqrt 3, u^4+2u^3-4u)27. lim(t-> sqrt 5, t^5-3t^3+t-1)28. lim(x-> root(3, 2), -x^6 +3x^3 -9)29. lim(u-> -sqrt 5, u^4+2u^3-u^2)30. lim(x->-2, x^14 + 7x^7 + 2)31. lim(x-> 4, x^7 +3x^4 +19)32. lim(x->2, x^15 + 4x^30)33. lim(x->2, x^14 + 3x^3 + 29)34. lim(x-> 1, x^20-2x^10+1)35. lim(x->2, x^100 + 2x^50 + 1)36. lim(x-> -3/2, (x-4)^10)37. lim(t-> 6, (3t-9)^100)38. lim(x-> 1/2, (4x-1)^50)39. lim(x-> -2, (x^2-2)^6)40. lim(x-> 1, (5x^2-x)^80)41. lim(x-> 2, (x^3-12)^5)42. lim(x-> 1, (x^3+2)^2)43. lim(x-> -1, (x^3+2)^2)44. lim(x-> 1, (3x^2-7x+3)^10)45. lim(x-> -2, -(x^3-1)^4)46. lim(x-> - 3, (x^2 - x+1)^3 )47. lim(t->-2,(t+1)^7(t^2-1))48. lim(t-> 2, (t-1)^3(t^2+1)^2)49. lim(t-> sqrt 3,(2t-1)^7(t^2-1)^3)50. lim(t-> - 1, (t-1)^8(t^2+1))1. lim(x->pi/2, x/3 - 1/7)2. lim(x->-2, (x^2-4)(x-2))3. lim(t->0, t(1+1/t))4. lim(u-> -1, (u^4+1) / (u^3-1))5. lim(x-> -1, (x+1)/(1-x^3))6. lim(x->1, (x-1)/(1-x^3))7. lim(x->0, (1-1/x^2)/(1-1/x))8. lim(x->1,x^2/(x-1) - 1/(x-1))9. lim(t->4, 2t/(t+4)+8/(t+4))10. lim(x->0, (1/(2+x)-1/2) / x)11. lim(x->2, (1/x - 1/2)/(x^2 - 4))12. lim(x->1, (x^2 + x - 2)/(x^2 - 3x + 2))13. lim(x->2,(1/x-1/2)/(x-2))14. lim(h->1/2, 2h/(h + 1/h))15. lim(x->0+, sqrt x - 3)16. lim(x->2-, x sqrt (4-x^2))17. lim(x->2+, sqrt (x^2-4))18. lim(t->4, sqrt t - 1/sqrt t)19. lim(t->2, (3t^3+4t - 5)^(1/3))20. lim(x->3-, x sqrt (9 - x^2))21. lim(x->64, (x^(1/3) - sqrt x)^2)22. lim(x->1, (3x - sqrt (x+1))^(5/3))23. lim(u-> -2, sqrt (u^4-4u+1))24. lim(x->2, (x^2+4)^(-1/3))25. lim(x->1, (sqrt x +1/sqrt x)^5)26. lim(x->8, 2x^(1/3) - 8x^(-2/3))27. lim(x-> -1, sqrt(x^3+2x+7))28. lim(r->3, (r^4-7r+4)^(2/3))29. lim(z->8, z^(2/3)/(z - sqrt (2z)))30. lim(x->1, (x - 1)/(sqrt x - 1))31. lim(x->9, (3 - sqrt x)/(9 - x))32. lim(t->0, (sqrt(2-t) - sqrt 2)/t)33. lim(y->0, (1 - sqrt (1+y))/(3y))34. lim(x->5, (sqrt x - sqrt 5)/(x - 5))35. lim(x->9, (x^2 - 81)/(sqrt x - 3))36. lim(x->-8, 4x^(2/3)/(4 - x^(4/3)))37. lim(t->4, (t^2 - 16)/(2 - sqrt t))38. lim(t->1, (root(3, t) -1)/(t-1))39. lim(x->64, root(3, x + 3 sqrt x))40. lim(t->9, (9 - t)/(3 -sqrt t))41. lim(x->0, (sqrt (x+4) - 2)/x)42. lim(x->9, (sqrt x - 3)/ (x^2 - 81))43. lim(x->16, (x - 16)/(2 - x^(1/4)))44. lim(x->0, ((8 - x)^(1/3) - 2) / x)45. lim(x->3, abs (1 - x))46. lim(x->sqrt 3, abs (x^2 - 8))47. lim(x->4, 3x^2 - 5 sqrt x - 6 abs x)48. lim(x->1, (abs (2x - 4))^(2/3))49. lim(x->4, abs (x/(2 - x)))50. lim(x->0, abs ((x+4)/(x - 2)))51. lim(x-> - 4, (x^2 - 16)/(abs x - 4))52. lim(x->1, (e^x +1)^2)53. lim(x->1, x^3 cos (1/x))54. lim(w->-2, root(3, (4w+3w^3)/(3w+10)))1. x^22. 1/x3. sqrt x4. 2x+35. -3x6. 4x+17. x^2 + 2x8. 1/x^29. 4x^2+1/x^210. 100-16t^211. 5y(100-y)12. x^2+113. x^2-x14. -3x^2+2x15. (4x+3)^216. x^317. x^3-2x^2+x-118. -2x^219. 5x-x^220. sqrt(1-x)21. sqrt (3x-1)22. sqrt (2x+1)23. sqrt (t+1)24. sqrt (10-t)25. 2x-3/x26. 1/(2x+1)27. 1/(x+1)28. 1/(5-2u)29. 1/(x^3)30. 1/(x^4)31. 1/x^232. 1/(x+3)33. x+1+1/x34. 1/sqrt x35. sin x36. cos x37. tan x38. x^3+x39. x^3-4x40. 1-x^341. x^3/3+x^2/2-542. 1-x+x^2-x^343. x^444. 2x^3+145. 3x^4 - 1/x46. x^3-4x47. (x+1)/(x-1)48. sqrt(1+3x)49. (1-x)/x^250. x^3-1/x^251. 1/x^2+11. x^2 - 12. 4pi r^23. -100 x^54. 3 x^1015. (1/8) t^2 + 206. (y^5) / 707. (4/3) pi r^3       @This is the formula for the volume of a sphere of radius r.8. t^2 - 6t + 99. x^2 -10 x + 10010. (1/2) t^2 + 3t + 211. 7x^2 -10 x + 1012. 2x^3 - 713. 7t^3 - 3t^2 + 614. 4t^3-9t^2 + 6t + 215. 2t^3 - 9t^2 + 6t + 216. y^3 - 2y^2 + y - 117. 1 + x + x^2 + x^318. x^4-4x+119. 11 u^5 - 6 u^3 - 820. 1 - t + t^2 - t^3 + t^521. x^4/2 - (3/2)x^2 + x22. 7t^3 - 3t^2 + 523. x^4 + 11x^3 - 9x^2 + x - 124. x^10 - x^9 - x^8 - 125. t^(36) + t26. x^4-4x^2-1527. u^6 +4 u^3 - 1228. x^10 - 3x^5 - x - 129. z(20 - z)       @Multiply out before differentiating30. (2u - 1)(u + 1)       @Multiply out before differentiating31. x^2(x + 3)       @Multiply out before differentiating32. (x^2 - 1)(x + 3)       @Multiply out before differentiating33. (x - 1)(x^2 + 1)34. x^2(x^3 - 4)35. (4t - 3)^2       @Expand the square before differentiating36. (3x + 2)^3       @Expand the cube before differentiating37. (x^2 + 1)^238. (x^2 - 2x)^2       @Expand the square before differentiating39. 3t (t^2+1)^2       @Although this is not a polynomial, it simplifies to a polynomial.  Simplify before differentiating.40. sqrt (3x^4)       @Although this is not a polynomial, it simplifies to a polynomial.  Simplify before differentiating41. sqrt (16x^8)42. 1 - x - (sqrt x)^4       @Although this is not a polynomial, it simplifies to a polynomial.  Simplify before differentiating.43. (sqrt x - x sqrt x)^2       @Although this is not a polynomial, it simplifies to a polynomial.  Simplify before differentiating.44. (2sqrt x + x^2 sqrt x)^245. (x^4+ 2x^3) / x^246. x^2 (x+1+1/x)       @Although this is not a polynomial, it simplifies to a polynomial.  Simplify before differentiating.47. (5x^2+2x) / x       @Although this is not a polynomial, it simplifies to a polynomial.  Simplify before differentiating.48. (x^3+3x) / x       @Although this is not a polynomial, it simplifies to a polynomial.  Simplify before differentiating.49. (x^8 - 8x^7)(x - 1/x)       @Although this is not a polynomial, it simplifies to a polynomial.  Simplify before differentiating.50. (x^(3/2) - 3x) / sqrt x       @Although this is not a polynomial, it simplifies to a polynomial.  Simplify before differentiating.1. 5/x^22. (2x - 1)(x+1)3. t^(-9)4. x^3 + 1/x5. (1+x^3)/x^36. 7 t / (1+t^2)7. (x+11) / x^38. 4u^4 - 1 / 4u^49. x^3 / (1+x^3)10. (4x - 7)^211. (x+12) x^312. (x-1) (x+1)^213. y(y+1)(y+2)14. 1 / (x - 1)+1 / (x+1)15. 3 / x^2 - 5 / x^3 +7x16. (x^2+x+1)^217. (x+x^2)(1+x^(-1)+x^(-2))18. (2+1/t)/(t - 1)19. (1 - 1/x) (1+2/x)20. (x^8 - 8x^7)(x+1/x)21. (x+1/x)(x - 1/x)22. (1 - 1/x)(1+1/x^2)23. 1 / (1 - 5/x)24. (1 - 1/x) / (1+2/x)25. 1 / (1+x+x^2+x^3)26. (x^2 - 1) / (x^2+1)27. (1/x - 4/x^3+7/x^4)28. (x^2+x+1) / (x^2 - 1)29. (7x - 1) / (4x+1)30. (x+1) / (x+1)^231. (x^3+1)^(-1)32. 1 / (a - 5x^(-3))       @Don't be confused by an extra letter in the problem.  Treat it as a constant.33. (5r - 1)^(-2)34. (1 - 1/x) / (x - 3)35. (2+theta^2) / (1 - theta^3)36. 1/ ((x^2+1)(x^2+x+1))37. (1 - x)(2 - x) / (x+3)38. (x+1)(x+2) / ((x - 1)(x - 3))39. (1+u)(1+u^2)^(-1)40. (x^2+x+1)/sqrt x41. t + root(3, t^2)42. sqrt(x) (x^3 - x+1)43. (sqrt x - root (3,x))(1 - root (5,x))44. sqrt t - 1/ sqrt t45. x^(1/2) / (x^2+4)46. x^(1/3) / (1 - x^2)47. (2x+1) / x^(2/3)48. 5t^(1/3) / (t^3+1)49. root (3, u^2) / (5u - 5)50. x^5 - root(5, x)51. x^100 + 50 x + 152. sqrt t - 1/ sqrt t53. x^4 - root(4, x)54. t sqrt t + 1/(t^2 sqrt t)55. t/(t+c/t)       @Don't be confused by an extra letter in the problem.  Treat it as a constant.56. ax^2 + bx + c       @Don't be confused by extra letters in the problem.  Treat them as constants.1. lim(x->pi/2, (sin x) / x)       @The denominator does not go to zero.2. lim(x->pi/4, (tan x)/(4x))       @The denominator does not go to zero.3. lim(x->pi/3,sin x + cos x)4. lim(t->pi/6, sec t tan t)5. lim(x->pi/2, csc^3 x)6. lim(x->pi, x^2 sec x)7. lim(u->pi, sin^2 (2u) + cos^3 (3u))8. lim(x->2, sin (1/x - 1/2))9. lim(x-> 0, x csc x)10. lim(x->0, x sec x)11. lim(t->pi/3, (sqrt 3) sin t - 2t)12. lim(x->0, x^2 sin x)13. lim(t->-3pi,t^3 sin^4 t)14. lim(x->0, (sin x)/(5x))15. lim(t->0,(sin 3t)/t)       @Make a substitution so you can use the formula for $sin(x)/x$.16. lim(t->0, 3t / sin t)       @No substitution is necessary.  Just pull the 3 out.17. lim(x->0, x cot x)       @This can be converted to $x/ tan(x)$18. lim(u->0+, (sin u) / sqrt u)19. lim(x->0, (1/x^2) sin (2x^2))       @Make a substitution so you can use the formula for $sin(x)/x$.20. lim(x->0, x sin (1/x^2))       @Make a substitution so you can use the formula for $sin(x)/x$.21. lim(x->0, sec x + tan x)22. lim(x->0, x csc x)23. lim(x->0, (sin^2 x) / x)       @Make a substitution so you can use the formula for $sin(x)/x$.24. lim(x->0, sin (x^(1/3)) / x^(1/3))       @Make a substitution so you can use the formula for $sin(x)/x$.25. lim(x->0, 3x / tan (5x))       @Multiply numerator and denominator by something to make it $sin (u)/u$.26. lim(t->0, (sin^2 t)/t^2)       @Make a substitution so you can use the formula for $sin(x)/x$.27. lim(x->0, (cos x^2 - 1) / x^2)       @Make a substitution so you can use the formula for $(1-cos u)/u$.28. lim(x->0, sin(2x)/cos x)29. lim(x->0, (2 sin x cos x) / x)       @Pull out the cosine term leaving $sin(x)/x$30. lim(x->0, (sin 4x) / tan 3x)       @Intuitively, when $x$ is small this is about $4x/3x$, so the answer is $4/3$. But it's not so easy to prove it!$31. lim(theta->0, (sin^2 theta)/theta)       @Multiply numerator and denominator by something to create $sin (u)/u$.32. lim(t->0, t^5 / (tan^5(t)))33. lim(t->0, t^3/(tan^3(2t)))34. lim(t-> 0, t^2 cos (1/t))       @You can't work directly with $cos(1/t)$, so make it $cos u$ first35. lim(t-> 0, root (3,t) sin (1/t))       @You can't work directly with $sin(1/t)$, so make it $sin u$ first36. lim(x-> 0, (x^2 cos x) / sin^2 x)       @Simplify a complicated limit like this one by first pulling out any factors with nonzero limits.37. lim(x-> 0, (1 - sec x) / (x sec x))       @The denominator goes to zero, so you must simplify the expression first.38. lim(t-> 0, t sec t csc t)       @Since $csc t$ is undefined at zero, you must simplify first.39. lim(x-> 0, (x cos^2 x + x sin^2 x - x) / tan(x))40. lim(t-> 0, (3t - cot t) / (t+2 cot t))41. lim(u-> 0, (sin u) / (1+cos u))42. lim(x-> 0, (x cos x - x^2) / (2x))43. lim(x-> 0, sqrt(cos(x)) sin (x)/x)1. 2cos x - tan x2. sin x + cos x - 13. 2 cos x - sin x4. sin x + 3cos x - 45. (2 tan x - csc x)/56. sin t sec t7. cos x sin x8. csc y sec y9. sin x cos (2x)10. csc x cot x11. (1 - cos x)(1 + cos x)12. 2 cos x - 4 x^213. x sin x14. x tan x15. x^3 cos x16. (1 - x^2) sin x17. 3 u^(1/3) cos u18. (x + x^2) sin x19. x^(1/2) sin x + x^(-1/2) cos x20. x^2 (sin x) (cot x)21. sin(x) / x22. (1- cos^2 x)/sin x       @Simplify before differentiating23. sin^2 x24. tan^2 x25. cos^3 x26. sin(sqrt x)27. tan(sqrt x)28. sqrt(sin x)29. root(3, sin x)30. sin(cos x)31. (cos x) / x32. (sin x) / (x^2 + 1)33. 1/(2sin x+3)34. 1 / (sin x cot x)35. 1 / (sin x tan x)36. (1 - cos y) / (1 + cos y)37. (cot x) / (1 - tan x)38. (sin x)/(1+cos x)39. (cot theta) / (1 + cot theta)40. (cos t) / sqrt t41. x^3 cos^3 (x)42. csc x sec^2 x43. (sin^2 x) / x^244. (sin x)/(1-cos^2 x)45. cos (x^2)46. sqrt (1 + tan u)47. sqrt(sec(x))48. cos(sqrt x)1. (1-6x)^32. (x^3-x)^53. (x-x^3-x^5)^44. (x+1/x)^35. (t^(-1)+t^(-2))^46. (x^3/3+x^2/2+x/1)^(-1)7. ((6x+x^5)^(-1)+x)^28. (1+(1+x)^3)^49. (z^2-1/z^2)^610. ((x+1)/(x-1))^511. (x/(1+x^2))^712. sqrt(x^3 - 3x)13. sqrt (csc 2s)14. sqrt (6x^2+3)15. sqrt ((3x+2)/(5x-2))16. sqrt (x^3/(x+3))17. (6 sqrt x+3)^318. sqrt (3x+2)/ sqrt (5x-2)19. (sqrt (x^2-1))/x20. (t - 1/t)^(5/2)21. (8x-7)^(-5)22. (2x+1/x)^(-6)23. sin (x^2)24. (1/t+1/t^2+1/t^3)^(-4)25. tan(3x)-526. sin (-x) - cos (-x)27. sin(3x) - tan(5x)28. cos x sin(4 x)29. sin^5 x30. tan^8 x31. sin x^532. (2+sin 2t)^433. (tan 2x)^934. tan^6 (x)35. cos^2 (x^2)36. (sin u) cos^2u37. (sec x+tan x)^(-1)38. sqrt (1 + tan 3u)39. sqrt (sec 2x)40. sin^5 (sqrt x)41. ln (1+cos r)42. e^(x^2-x)43. cosh (sin x)44. ln^3(x^2+7)45. e^ln x46. e^(x^5)47. e^(-sqrt x)48. ln (ln t)49. e^cos x50. e^(-1/x)51. 3^(5x-7)52. cos (sin x)53. sin (cos x)54. sin (1/x - 1)55. sec (cos (sqrt x))56. cos ((cos^2 x - 1) / x^2)1. x/(6x+4)^(2/3)2. (8x)^(1/3)+(8x+2)^(1/3)3. (x+1)^(-2) (x-5)^(-1)4. sqrt(x^2 + 1)5. x sqrt x6. 1/(x^2+1)7. x/(x^2+1)8. 1/(x^2-1)9. x/(1-x^2)10. sin^3 x + cos^3 x11. (cos^2 x + 2)^(-2)12. (x^2 - cos^2 x)^213. sin^(-2)x14. ((sin x)/(1+cos x))^215. (1+cot x)^(-6)16. (sin 5x-cos 5x)^517. tan(5-6x)^(1/3)18. tan^2(theta) sec^3(theta)19. sin^2(sqrt x)+cos^2(sqrt x)20. sin^2 (theta) + cos^2 (theta)21. 1 + tan^2 (theta)22. 1 - 2 cos^2 (x/2)23. tan^2 (x/2) - sec^2 (x/2)24. cos^2 (x) - sin^2 (x)25. sin (theta+sin theta)26. cos (1+tan 2x)27. (6t^2 + 5)^3 (t^3-7)^428. sqrt (x+ sqrt (x+ sqrt x))29. e^(sin(x^2+1))30. sin (e^(x^2+1))31. sin(x)/x32. cos(x)/x33. sin(x)/x^234. sin(x^2)35. cos(x^2)36. e^(sin x)�5..6;	5f.2=V	5�.tz	5�.��	5�.I��	�V	5
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