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�� � � P � � � �C �� ���� � � yi��C ��_� write as square write as cube express in form a^? Assuming the new square roots are defined. The resulting expression is equal to the previous one only subject to those assumptions. For example, its graph may be different. You can only convert a specific, numerical angle to degrees. Definition of a new variable cannot be constant. The group entered must be a sum. $a\sqrt b = \sqrt (a^2b)$ if $a\ge 0$ The factor outside the square root must be nonnegative The factor outside the root must be nonnegative $$a root(n,b) = root(n,a^n b)$$ (n odd) $$a root(n,b) = root(n,a^n b)$$ ($a\ge 0$) Would you like to regard the variables occurring non-linearly as constants and proceed to solve for the other variables? Inappropriate problem Too many windows You have solved the equations, but perhaps the answers should be simplified. You have solved the equation, but MathXpert would take one more step. You have solved the equation, but perhaps the answer should be simplified. Because the topic is Trig Addition, a solution using a trig addition formula will be given, instead of a shorter solution using periodicity. Although a formula for the singularities has been calculated, it was too hard for MathXpert to find their numerical values. MathXpert calculation MathXpert graph Please enter a positive integer. Zero is not positive. $-^n\sqrt a = ^n\sqrt (-a)$ if n is odd The original cubic must have more than one real root. In that case complex solutions of the equations you have derived will give rise to real solutions of the original equation, but complex numbers are not used in this topic. There can be at most three roots of a cubic equation. Simplify the expressions for the roots until some of them are identical. rationalize denom and simplify Enter the new exponent: You have solved the equation, but the answer should still be simplified. The selected topic requires MathXpert PreCalculus Assistant. The selected topic requires MathXpert Calculus Assistant. Illegal topic for Algebra Illegal topic for Precalculus The file %s is read-only. You cannot write into that file. The file %s already exists. Do you wish to replace it? The file %s is a hidden or system file. You cannot open it. The file %s cannot be opened. Probably the file is damaged. Too many files already open. Close files open in other applications. Directory %s does not exist. %s is not a legal filename. File %s does not exist. The function values could be calculated only at isolated points, so no graph is visible. The reason could be that some intermediate numbers were too large or too small, or it could be that the function is really only defined at isolated points. File is not a valid MathXpert document. Complex numbers are not in use. This law is not valid for real roots. Too many solutions will result. substitute specific integers a=-b becomes $a^2=-b^2$ if $a,b \ge 0$ a=-b becomes a=0 if $a,b \ge 0$ a=-b becomes b=0 if $a,b \ge 0$ A function with that same name has already been defined. You can redefine it or undefine it, but not define it. from file $lim(t\to \pm \infty ,cos t)$ is undefined $lim(t\to \pm \infty ,sin t)$ is undefined $lim(t\to \pm \infty ,tan t)$ is undefined Limit of the denominator is not defined and not plus or minus infinity. Limit of the numerator is not defined and not plus or minus infinity. $a/^n\root b = ^n\root (a^n/b)$ (n odd or $a\ge 0$) $^n\root a/b = ^n\root (a/b^n)$ (n odd or $b>0$) $(\sqrt a)/b = \sqrt (a/b^2)$ if $b>0$ $a/\sqrt b = \sqrt (a^2/b)$ if $a\ge 0$ Numerator must be non-negative Denominator must be non-negative Enter the first new exponent: First evaluate the derivative. File No equation is solved for a derivative of a variable. eliminate derivative You have already differentiated the equation. You must solve each equation, either for a derivative or a variable. Limit of denominator is undefined. Is This law is not generally valid; what is under the root must be real. What is under the root must be negative. sg(x) = 1 if x > 0 sg(x) = -1 if x < 0 sg(x)=|x|/x (x nonzero) sg(x)=x/|x| (x nonzero) d/dx sg(u) = 0 (u nonzero) $\int sg(u)v dx=sg(u)\int v dx$ (u nonzero) Expression inside sg may be zero. The expression inside the sg function cannot be positive. sg(x)=1 assuming x>0 The expression inside the sg function cannot be negative. sg(x)=-1 assuming x<0 Enter n = integer - k, where n is the variable to change. sg(ax) = sg(x) if a>0 sg(ax) = -sg(x) if a<0 sg(ax/b)=sg(x), a/b>0 sg(ax/b)=-sg(x),a/b<0 MathXpert cannot calculate that limit. The resulting numerator and denominator would both be undefined. The resulting numerator and denominator would both be zero. The resulting denominator would be zero, and MathXpert can't determine its sign. Multiply one factor and divide the other by what? One limit would be zero and the other undefined. Format of mathpert.toc is illegal. If you altered it, restore the original. If not, reinstall MathXpert. That expression is real, but it is negative, so it's not in polar form, which is $re^(it)$ with $r$ positive. That expression still contains a product of trig functions. Initial value of function Initial value of derivative Initial value of second derivative Initial value of third derivative Initial value of fourth derivative First evaluate the limit. $lim a/u^2 = \infty $ if $lim u = 0$ and $a > 0$ $lim a/u^2 = -\infty $ if $lim u = 0$ and $a < 0$ $lim a/u^2^n = \infty $ if $lim u = 0$ and $a > 0$ $lim a/u^2^n =-\infty $ if $lim u = 0$ and $a < 0$ $lim u^n = (lim u)^n$ requires $lim u$ to be defined, infinite, or oscillatory, MathXpert cannot verify either condition. That is not the case here. Eliminate zero denominators. or when $u$ is nonnegative or nonpositive. Evaluate to apply the divergence test $lim uv = lim u lim v$ can fail if $lim u = 0$ and $lim v$ is undefined. Enter one term of the new sum: This inequality is too complicated for MathXpert to graph. $a < \sqrt u$ iff $0 \le u$ provided a < 0 $a \le \sqrt u$ iff $0 \le u$ provided $a \le 0$ $\sqrt u > a$ iff $u \ge 0$ provided a < 0 $\sqrt u \ge a$ iff $u \ge 0$ provided $a \le 0$ $a < ^2^n\sqrt u$ iff $0 \le u$ provided a < 0 $a \le ^2^n\sqrt u$ iff $0 \le u$ provided $a \le 0$ $^2^n\sqrt u > a$ iff $u \ge 0$ provided a < 0 $^2^n\sqrt u \ge a$ iff $u \ge 0$ provided $a \le 0$ One of the factors is zero. One of the factors is, or simplifies to, zero. If not, you may get a wrong answer, so be careful. MathXpert will assume it is defined and nonzero. MathXpert is assuming that what is under the square root is nonnegative. It is possible to make contradictory assumptions and arrive at wrong answers. Therefore, keep an eye on your assumptions. Base of exponent must be positive. There is an unevaluated infinite or undefined subterm. Denominator too complicated to expand in partial fractions. you must first prepare for it by using Before you are ready to use You might try !This equation can be solved for the original integral. !provided this limit turns out to be zero. Input not acceptable $(e^(-t)-1)/t\to $ $(sinh t)/t\to $ $(tanh t)/t\to $ $(cosh t-1)/t\to $ $(1-cosh t)/t\to $ $(cosh x-1)/x^2\to \onehalf $ as $x\to $ Disabled Restricted Trial The problem file for this topic has been altered. Restore the original problem files or reinstall MathXpert. from Previous Next Help Edit Paste Problem Number Source Equations valid for all times: Equations valid for only one time: Graph Number Domain and Range Style Riemann Sums From to Number of Intervals Style of Sum Simpson's Rule Trapezoid Rule Is this what you meant? Point and Slope Original Current Slope Selected Point Active is now with increment After parameter changes Erase old graphs Show all graphs Parameters Initial Values After changing initial values Graph Colors Color Border Function Background Axes with Title is Ranges Horizontal Vertical First Graph Second Third Fourth Fifth Sixth Restore Original Parametric Graph Ranges Parameter Ensure circles are round Polar Graph Ranges Angle Textbook Selection Select a textbook About MathXpert Design and implementation: Michael Beeson Lab Edition Book dialog: Dave Empey Translation: Splash screen art: Cindi Shih Copyright © 2004 Help With Math Please wait Print Left Header Right Header Size and Position of Graph Inches Centimeters Left Margin Top Margin Close this calculation? Don't ask this question in the future If you turn off confirmation here, you can turn it back on from the Options menu. Open problem file Close problem file Open .mxp file Exit Save Save as Print now Assumptions Author's Commentary Functions Define a function Redefine a function Undefine a function Show functions Always request confirmation Never request confirmation Formulas Highlighted Formulas Selected Formulas Justifications Restore Factory Colors Type Size Bigger Smaller Normal Tool Bar Large Icons Small Icons Decimals Large Numbers Sound On Off Confirm Close Language Operations Show Operations Menu Hide Operations Menu Cascade Tile Arrange Icons Close All Contents Search for Help on... Using help Ticks None Multiples of Pi Axes Labels Numbers Letters No Labels Change Colors All Graphs Singularities Jumps Hide Titles Show Grid Approximate Integration Differential Equations $^n\sqrt (-a) = -^n\sqrt a, n odd$ $a<u^2<b$ => $-\sqrt b<u<-\sqrt a$ or $\sqrt a<u<\sqrt b$ $a\le u^2\le b$ => $-\sqrt b\le u\le -\sqrt a$ or $\sqrt a\le u\le \sqrt b$ $a<u^2\le b$ => $-\sqrt b\le u<-\sqrt a$ or $\sqrt a<u\le \sqrt b$ $a\le u^2<b$ => $-\sqrt b<u\le -\sqrt a$ or $\sqrt a\le u<\sqrt b$ $a < u^2^n$ iff $u<-^2^n\sqrt a$ or $^2^n\sqrt a<u$ $a\le u^2$ iff $u\le -\sqrt a$ or $\sqrt a\le u$ $a<u^2^n<b$ => $-^2^n\sqrt b<u<-^2^n\sqrt a$ or $^2^n\sqrt a<u<^2^n\sqrt b$ $a\le u^2^n\le b$ => $-^2^n\sqrt b\le u\le -^2^n\sqrt a$ or $^2^n\sqrt a\le u\le ^2^n\sqrt b$ $a<u^2^n\le b$ => $-^2^n\sqrt b\le u<-^2^n\sqrt a$ or $^2^n\sqrt a<u\le ^2^n\sqrt b$ $a\le u^2^n<b$ iff $-^2^n\sqrt b<u\le -^2^n\sqrt a$ or $^2^n\sqrt a\le u<^2^n\sqrt b$ $\sqrt (a^2^n)=a^n$ if $a^n\ge 0$ $|sin u| \le u$ if $u\ge 0$ $|arctan u| \le u$ if $u\ge 0$ $|tan u| \le u$ if $0\le u\le \pi /2$ $$lim(x->a,c)= c$$ (c constant) $$lim(x->a, c^v)=c^(lim(x->a, v))$$ (c constant > 0) compute factorial shift sum limits $\sum cu = c\sum u$ (c const) proved by induction defn of $d^nu/dx^n$ differentiate matrix for power series $\sqrt a/b = \sqrt (a/b^2)$ if b>0 $\sqrt a/b= -\sqrt (a/b^2)$ if b<0 (b>0 or n odd) (b<0, n even) if $a\ge 0$ if $a\le 0$ (n odd or $a\ge 0$) (n even and $a\le 0$) if $-\pi /2\le \theta \le \pi /2$ if $0\le \theta \le \pi $ is undefined $\sqrt (-a) = i\sqrt a$ if $a\ge 0$ Number inside ln must be in polar form. Number inside $\sqrt $ must be in polar form. Number inside $^n\sqrt $ must be in polar form. Use "clear denom of i" instead [p=a,p=-a] and $p\ge 0$ iff p=|a| |u| = u iff $0 \le u$ |u| = -u iff $u \le 0$ $0\le u/v$ => 0<uv or u=0 $u/v\le 0$ => uv<0 or u=0 (if n is odd) $u^2<a iff -\sqrt a < u < \sqrt a$ $a<u^2 iff u<-\sqrt a or \sqrt a<u$ $a\le u^2 iff u\le -\sqrt a or \sqrt a\le u$ $-a<x^2<b$ iff $x^2<b$ $-a\le x^2\le b$ iff $x^2\le b$ $-a<x^2\le b$ iff $x^2\le b$ $-a\le x^2<b$ iff $x^2<b$ $u^2^n < a$ iff $-^2^n\sqrt a < u < ^2^n\sqrt a$ $u^2^n \le a$ iff $-^2^n\sqrt a \le u \le ^2^n\sqrt a$ $u^2\le a iff -\sqrt a \le u \le \sqrt a$ cancel cancel gcd polynomial division Divide row by Add times row to row Sub from row matrix multiplication formula for 2 by 2 matrix inverse compute inverse convert matrix eqn where cos in $a|b| = |ab|$ if $0 \le a$ a|b|/c = |ab/c| if $0\le a/c$ Completing the square requires a non-constant linear term. This equation is solved, but it is customary to put the variable on the left side, so MathXpert would take one more step. OK !Assuming the previous right side is nonnegative. Find the extrema on You must compute a table of function values and select the maximum or minimum. You should select the maximum and/or the minimum to complete the problem. !No minimum or maximum on this interval Find the extrema. This operation cannot be applied to an improper integral unless the integrand is nonnegative. There is an unevaluated infinite series. MathXpert cannot find a closed form for this series. The general term does have a finite limit. telescoping series MathXpert cannot compute the limit of the general term. Expression to shift by cannot depend on the index variable. (n odd) function is constant Max and min are the same for a constant function. It is not necessary, and will not help, to take the derivative. Perhaps you are trying to reject an endpoint. You can't insert more than 1000 new terms. add to index variable subtract from index variable How many terms do you want explicitly written out? Decrease the lower limit of summation by how much? Add what to the index variable? Subtract what from the index variable? Decrease lower limit MathXpert cannot check the convergence of the series that would result. The resulting series would be divergent, so the law cannot be applied. The function being defined cannot be used in the definition. Evaluate to apply the integral test Evaluate to apply the root test Evaluate to apply the ratio test Evaluate to apply the comparison test The general term is not decreasing. MathXpert cannot determine that the general term is decreasing. !The series is convergent. !The series is divergent. Some assumptions have been made. !The test was inconclusive. finish integral test finish root test finish ratio test finish comparison test finish divergence test You must first evaluate the limit, or undo. The comparison term does not contain the summation variable. Evaluate to apply the limit comparison test finish limit comparison test The test worked; the problem is reduced to the convergence of this series. Cannot verify the required inequality Enter the general term of the comparison series The new integrals would not be defined, so this operation is illegal. The integrand is not defined on the entire interval of integration. You should break it into two or more integrals first. The integrand is undefined somewhere besides the left endpoint. The integrand is undefined somewhere besides the right endpoint. MathXpert cannot evaluate the limit. The limit is zero. limit of integrand is not zero Although there are singularities, the integrand is nonnegative, so the integral is infinite rather than just undefined. There are singularities. You might be able to get the answer $\infty $ or $-\infty $ if you first break the integral, unless it contains infinities of both signs. When both limits are infinite, you must break the integral first. The limits at the two ends must exist separately. limit of integrand is undefined condensation test finish condensation test !The test worked. The series is convergent. Assumptions may have been made. !The test worked. The series is convergent. !The test worked. The series is divergent. The limit of the general term is not zero. You started the divergence test, but didn't finish it yet. You started the integral test, but didn't finish it yet. You started the comparison test, but didn't finish it yet. You started the limit comparison test, but didn't finish it yet. You started the condensation test, but didn't finish it yet. You started the root test, but didn't finish it yet. You started the ratio test, but didn't finish it yet. The convergence or divergence is not yet settled. calculate first terms Maximum number of first terms to add is about 128,000. Lower index of sum cannot exceed sixteen million. Calculate the sum of the first how many terms? !If this series converges, so does the original series. !If this series diverges, so does the original series. The answer must be expressed in terms of the original variable or variables. is not correct. Cannot switch to that language. express series as $a_0 + a_1 + ...$ express series as $a_0 + a_1 + a_2 + ...$ express series using ... and general term show more terms before ... express series using sigma notation show another term before ... The maximum number of terms before ... is 1000. How many more terms do you want to see? solve for constant of integration The resulting series would not converge. The resulting series would converge only at isolated points integrate power series term by term differentiate term by term MathXpert cannot open the file %s. It may be in another folder, or the name may have been misspelled. If you clicked on a Web page to open a MathXpert document, the hyperlink is not valid. You must first rename one of the summation variables. multiply series multiply power series divide power series add series subtract series Lower limits of summation are not the same. Upper limits of summation are not the same. You must rename one or more of the summation variables first. binomial series First rewrite one or both of the series, to arrange that the exponents have the same coefficient of the summation variable. First term in the denominator must be the constant term. MathXpert requires numerical coefficients for series division. Constant term must be nonzero for series division. There are too many function definitions. Undefine a function to make room for the definition of the coefficients of the quotient. MathXpert cannot verify that the recursion will terminate. Function argument must be an integer. Function argument too large. compute function value show terms with factorials evaluated show coefficients in decimal form do not use decimal form for coefficients do not evaluate factorials MathXpert requires numerical coefficients for series exponentiation. Exponent must be a number. express $(\sum a_k x^k)^n$ as a series Leading coefficient must be nonzero for series exponentiation. if otherwise express as power of ? Enter the desired base: Cannot draw the graph Function is not a non-constant polynomial for the current parameter value. Change the parameter value. Function is not a non-constant polynomial for the current parameter values. Change the parameter values. It is not correct to apply this operation to an improper integral. Select problem file Find the minimum and maximum of on the interval Cannot open problem file The specified problem file could not be found or is incorrectly formatted. Sorry, the term you entered is not a factor. The law $ln ab = ln a + ln b$ is not always correct. The two sides can differ by a multiple of $2\pi i$ . For example, try the case when $a$ and $b$ are both $-1$. !Assuming that the radius is positive. Range Redraw Prev &Undo &Hint Auto&Step Sho&wStep &AutoFinish &Finished &Graph &Prev &Edit &Next UHSWAFGPEN graphs Integration by parts cannot be applied to improper integrals directly. First express the integral as a limit. That function is still in use. To redefine it you must first close all calculations and graphs that mention it. Can't verify exponent is even. Exponent is not even. Solution(s) should be reduced to the form $a + bi$. Division by zero is not allowed. That would produce the useless equation 1 = 1, since any nonzero number to the zero-th power is 1. That would produce the useless equation 0 = 0, since zero raised to any nonzero power is zero. That would produce a fraction with zero in the denominator, which is not defined. That expression is already in the form $u+iv$. Expression should be reduced to the form $a + bi$. result of comparison test You still need to state the final result of the comparison test for the original series. Red Gray Blue Green Cyan Magenta Yellow White Black thin thick no ticks normal ticks ticks at n pi Please use a color different from the background. and $-a \le u \le a$ iff $|u|\le a$ $-a < u < a$ iff $|u|<a$ MathXpert Algebra Assistant MathXpert Precalculus Assistant MathXpert Calculus Assistant by Select Graph Paper Adjust to Graph Paper Automatically adjust colors Title Title Background Light blue Medium blue Light orange Light green Medium gray Light gray Light yellow Light violet Apply changes to Graph 1 Graph 2 Graph 3 Graph 4 Graph 5 Graph 6 Please use a title color different from the background. Please use an axes color different from the background. Please use a border color different from the background. Please use a function color different from the background. Please use function colors different from the background. Width Height Landscape Portrait Whole page, with specified margins Maximum size Same shape as on screen Center vertically Center horizontally Save settings without printing Left margin plus graph width cannot exceed paper width. Top margin plus graph height cannot exceed paper height. Graph width must be positive. Graph height must be positive. tan(t/2) is undefined somewhere in the interval of integration. MathXpert cannot verify that tan(t/2) is defined on the interval of integration. Negative real numbers have no complex square roots. $(a^(it))^c = a^(it)^c$ only when $-\pi < t \le \pi$ First write a in polar form. Cannot redefine a built-in function. Equality sign expected. $\sqrt(bi)= \sqrt(b/2)+\sqrt(b/2)i$ if b >= 0 $\sqrt(-bi)= \sqrt(b/2)-\sqrt(b/2)i$ if b >= 0 $\sqrt(a+bi)= \sqrt((a+c)/2)+\sqrt((a-c)/2)i$ if b >= 0 and c=\sqrt(a^2+b^2) $\sqrt(a-bi)= \sqrt((a+c)/2)-\sqrt((a-c)/2)i$ if b >= 0 and c=\sqrt(a^2+b^2) There is a repeated variable on the left side. You have already used that letter on the right side of another definition. ac=bc iff a=b or c=0 Cannot redefine a function that is in use. Close all calculations or graphs that use this function, then redefine it. The selected expression must contain the variable of integration. The file you tried to open contains a user-defined function that is already defined. First close any open documents and choose Function | Undefine function from the menu, then try again to open this file. Exit MathXpert Make a Graph Work a Problem Run a Demo Point, Slope, Parameter Radians Degrees Go to Help With Math's web site Send email to Help With Math Author's essay about MathXpert Switch MathXpert to the specified language Double vertical range Halve vertical range Double horizontal range Halve horizontal range Enter the new lower limit of summation: We keep only one of the two solutions, since each of the two will generate the same solutions of the cubic equation. Grapher You are not currently enrolled in any course using WebGrades. Cannot get an answer from the server. Are you connected to the internet? If you are, then something else went wrong. Please try again later. If this problem persists, send email to contacthelpwithmath@gmail.com for help. You must enroll in WebGrades before this version of MathXpert will run. Your instructor will tell you how to enroll in WebGrades. evaluate Bernoulli number exactly evaluate Euler number exactly MathXpert cannot decide whether this series converges or not. The series must be absolutely convergent, and MathXpert cannot verify that it is. !We will try to prove the series converges. !We will try to prove the series diverges. %�|� 4 I: ; I ! I7 I & I $ > $ > .�@: ;'I?
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