# Tagged Questions

Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.

158 views

### Different results of the integrate $\int \frac{\sin (\pi s)}{(s-0.5)^2+90} \,ds$?

Following results are given of big different values. I think NIntegrate's one is right but others are not explained. ...
156 views

I have: ...
55 views

### Better to have infinities in limits or integrands (NIntegrate)? [closed]

I'm using ListPlot to plot the integral of a function with respect of the function's second variable: ...
157 views

### Numerically integrate and plot $f(x;p)$ for a range of the parameter $p$

Suppose we have an integral of the form $$I = \int_a^b dx \, \sin(px), \tag{1}$$ where I've take $f(x;p) = \sin (px)$ to be specific. I want to plot this integral for a range of values of the ...
410 views

### How much time should one give Mathematica for an integral evaluation?

Sometimes when I do integrals in Mathematica (M), it keeps thinking and thinking and I have no idea what is going on inside M. For how long should one wait or how does one know whether M has not got ...
42 views

### Which type of integrals are better for Mathematica [closed]

Is it in general better to type in a integral with its limits, or is it better to type an indefinite integral into Mathematica? With better I mean: Likelihood that Mathematica can solve it, ...
77 views

### repeat calculate [closed]

I want　to calculate the below program x[t+1].But I can only calculate t=0,1. please tell me how to calculate t = 0 to 10. ...
431 views

### Laplacian and DiracDelta

It is known that: $\nabla^2 \dfrac{1}{|r-r'|} = - 4 \pi \delta^3(\vec{r}-\vec{r}')$. If I do that with Mathematica, I find: ...
303 views

### Traces of the level surface $z=4x^2+y^2$

I came up with this method to plot the traces of the surface $z=4x^2+y^2$, in this case for $z=1$, 2, 3, and 4. ...
135 views

### Given integral, how to plot

I want to use mathematica to visualise some plots, this would help me understand my calculus course. My problem is this: Given that x^2 + y^2 <= a^2 Find ...
308 views

### Derivative of contour in ContourPlot

Sorry to bring this question up again, since there are many similar questions on the site. I use to think this is a easy job to do, because for the worst case I can follow the answers on this site. ...
426 views

### Why Mathematica cannot apply The Fundamental Theorem of Calculus automatically?

For some reason Mathematica cannot evaluate this definite integral: ...
277 views

### Fitting a Parametric Curve

I apologize if this question is obvious or simple. I'm in high school and have started playing around with Mathematica only recently. For my Calculus Final, I am supposed to use rotation about the $y$...
123 views

### Meaning of Pattern at derivatives of arbitrary functions

I want to derivate some general functions like D[F[x[r_, p_], y[r_, p_]], r] or this simpler one D[F[G[x_]], x] . When I ...
87 views

### Using Manipulate to determine intersection of two surfaces

Here is what I have done thus far: ...
251 views

### Strange Boundary NDSolve Problem

Mma10.1 doesn't work with the following boundary problem: ...
877 views

### Integrate gives wrong results

Integrate[a/(Sin[t]^2 + a^2), {t, 0, 2 Pi}] $$\int_0^{2 \pi } \frac{a}{a^2+\sin ^2(t)} \, dt$$ gives $0$ This cannot be true. What is going on? If I insert a ...
251 views

### Volumes of Revolution with detailed diagram

All, In calculus I have to do images such as the following in helping explain technique to students. This one is by rotating $y=\sqrt x$ about the x-axis, an image copied from Stewart's Calculus ...
90 views

### Adding a title that includes angle between two vectors in Graphic in Manipulate

Here is what I have tried thus far: ...
54 views

### Integration problem: lrgexp

I want to calculate the following integration but it gives the error PolynomialGCD::lrgexp: Exponent is out of bounds for function PolynomialGCD. The code is: ...
147 views

### Derivative of Continuous and Differentiable Piecewise function is indeterminate

I'm attempting to analytically stitch together two linear functions with two quadratic functions. The function I'm considering, then, is a piecewise function consisting of 4 parts. Below are the ...
130 views

### same code different results on different computers

This very simple code: ...
47 views

### Computing an inexact derivative with some terms preserved in exact form

I am beginning to learn Mathematica and have the following question: How can I return a derivative with exact numbers instead of one involving numerical approximations? My original, single variable ...
138 views

### Limit of a fractional integral

I am trying to find the limit for λ -> 0 of the integral listed below, but Mathematica give me only a ConditionalExpression ...
246 views

### Asymptotic forms of Bessel function

I want to replace Bessel functions by asymptotic forms, so the question is: can I find the best ones with help of Mathematica? And if it's possible, how can I do it? Update How can I get with ...
93 views

### Does DynamicModule cure Problem with Manipulate?

Hopefully, this is a final cure for the Problem with Manipulate introduced on A problem with Manipulate and then continued on Continuation of a Problem with Manipulate. Michael E2 suggested on the ...
219 views

### Speed up derivative evaluation

I'm trying to calculate the normal vectors and the tangent vectors at the discrete points of a suface. For example: ...
156 views

### How can I improve the solution of my PDE?

I want to improve the last code to find a better solution for umi. For now I'm using only MaxStepFraction. Also, when I put no ...
91 views

### Continuation of a Problem with Manipulate

For the beginning of this discussion, see: A problem with Manipulate. Now, the final use of the Initialization command doesn't protect the Global workspace. What I am discussing is not a single ...
184 views

### Mathematica's steps towards the result of a definite integral

I am interested in this definite integral: \eqalign{\int_0^\infty {x^2 \log(1-e^{-x})}\; dx\cr } That is: ...
130 views

### NIntegrate and Sum give different results in summing functions

I am using these two functions: ...
556 views

### How is it possible to check if a function is even or odd?

I tried it like this: ...
66 views

### Bug (?) in Mathematica in Derivative of function with Abs [duplicate]

I encountered a weird problem with Derivatives in Mathematica, see the following code: ...
97 views

### Numerical integral speed

I have the following code to calculate a numerical integral for any given a, however it takes a very long time, even with adaptivemontecarlo, which is not accurate enough: ...
925 views

### A bug in Integrate

Integrate[(1 + 16 Tan[2 x - y]^2)/(1 + 4 Tan[2 x - y]^2), {x, 0, 2 π}] Mathematica (wrong) output is (tested under versions 8 and 10.0, took ~ 1 minute of CPU ...
121 views

### Missing zero in the CoefficientList

The following list has a length only 10 (not 11) CoefficientList[Series[ArcTan[x]/(1-x^2),{x,0,10}],x] {0, 1, 0, 2/3, 0, 13/15, 0, 76/105, 0, 263/315} It should ...
224 views

### Wrong Limit in Mathematica 10.0.0

Bug introduced in 9.0.0 and fixed in 10.0.1 Limit[(Log[(3+Sqrt[5])/2]/(2*Log[(1+Sqrt[5])/2]))^(-1-2*n), n -> Infinity] Mathematica (wrong) output: ...
220 views

### Wrong Limit with LaguerreL

Bug introduced in 7.0 and fixed in 10.2.0 Limit[(n! LaguerreL[n,-1]/(n^(n+1/4)/Sqrt[2]/E^(n-2 Sqrt[n]+1/2))-1) Sqrt[n], n->∞] Mathematica (wrong) output <...
213 views

### definite integration very slow

I have to perform definite integration of function of this kind : ...
149 views

### LogisticSigmoid residue bug?

Bug introduced in 10.0 and fixed in 10.2.0 On version 10.0 for arm: Residue[LogisticSigmoid[z],{z,I Pi}] gives 0 not 1. ...
194 views

### How to speed up a symbolic integration

I have a question about an integral. I wanna integrate this: ...
283 views

### Why does Mathematica say $\int_0^1\int_0^1\int_0^1\frac{1.0}{xyz}\,dz\,dy\,dx=0$?

Mathematica 9 says that $\int_0^1\int_0^1\int_0^1\frac{1.0}{xyz}\,dz\,dy\,dx=0$ and $\int_0^1\int_0^1\int_0^1\frac{1}{xyz}\,dz\,dy\,dx=0$. ...
67 views

### Problem with 'time dependent' functions [closed]

I'm just trying to make $\frac{dx}{dt}$ where $x= \rho \cos\theta \sin\phi$ where $\theta, \phi$ and $\rho$ are time dependent functions. ...
324 views

### Find exponential generating function from the first few terms

The function FindGeneratingFunction computes the ordinary generating function of a sequence, given a sufficient number of initial terms. I have two questions in ...
53 views

### Multidimensional integration does not work

I am trying to solve an integral over Cubic Birillioun Zone, but after taking a long time Mathematica give nothing in return and just repeating the integral form, here is my integral, ...
46 views

### Plotting partial sums of Taylor Function

I need to plot the partial function: $T_f(x)=\log 2+\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{2^kk}(x-2)^k$ for $n=2$,$n=4$ and $n=6$ on the same plot over the interval $[-\frac{1}{2},4]$ and also the ...
54 views

### Need help to solve this math question when x reach 0 [closed]

My son can home and ask me to help him with this equation: lim ((x-2)/(2x-1))^(1/x) x→0 I try to use /www.symbolab.com but its too complicated to solve this. Thanks with the help
779 views

### How can I evaluate surface integral in Mathematica?

$$\iint_{S^+}x^3dydz$$where $S$ bottom part of $$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$$ $S^+$ - outer side of $S$ \iint_{S^+}P(x,y,z)dydz = \iint_{S}P\cos\alpha dS,\ \; normal : \...