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

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13
votes
2answers
303 views

What kind of hypergeometric function is it?

I found a formula for an integral of a product of three Bessel functions at The Wolfram Functions Site: I cannot understand what kind of hypergeometric function it is. The Mathematica code given ...
3
votes
1answer
388 views

Evaluating double Integral

While trying to evaluate the integral $\int_{y=0}^{x_2}\int_{x=0}^{min(x_1,y)} n (n - 1) (1 - y)^{(n - 2)}dxdy $ , Mathematica does not seem to yield any results. ...
6
votes
4answers
518 views

How do I obtain the correct double limit?

The command Limit[(Sin[x^2] + Sin[y^2])/ (x - y) /. x -> 0, y -> 0] (* 0 *) I think that Mathematica finds the iterated limit instead of the double ...
2
votes
2answers
279 views

Write a function that returns the logarithmic derivative

How can we write a function that if we input an expression f, it returns the log derivative $\frac{1}{f} \frac{df}{dx}$. We have to use a conditional or pattern test so that the function accepts any ...
1
vote
1answer
113 views

Integration of a rational function

I am trying to solve the following rational integral (I got assistance here): $$\int_{-\infty}^{\infty}{\frac{a+x}{b^2 + (a+x)^2}\frac{1}{1+c(a-x)^2}}dx$$ where $\{a, b, c\}\in \mathbb{R}$. I would ...
2
votes
0answers
118 views

Is this result wrong because of calculation time? (and more questions about Assumptions)

I am confused with the Integrate Given by Mathematica. First let's see a one-dimensional case: ...
0
votes
1answer
178 views

Integrate of Heaviside Function returns an error answer

I try to evaluate an Integral of a Heaviside function, but it turns out with an erroneous output(zero). Here is my integral: ...
0
votes
1answer
105 views

Taking derivative of Euler relation [closed]

I have defined the following function, which is the Euler relation for $\cos\,x$. f[x_] := 1/2*(Exp[I*k*x] + Exp[-I*k*x ] ) I want to take the derivative with ...
9
votes
1answer
179 views

How to calculate this integral? Integrate[BesselJ[0, x - BesselJZero[0, 1]]/x, {x, -Infinity, Infinity}]

I tried to calculate the following integral, but it returned unevaluated. ...
13
votes
1answer
227 views

How do I get a general form for n-th derivative of a function? [duplicate]

I tried the following but it basically returns unevaluated: ...
4
votes
2answers
125 views

Strange behavior of Integrate

I'm trying to calculate the following integral using Mathematica 9.0.1.0 a11=Integrate[Abs[Sin[b+x]],{x,0,2*\[Pi]}] This should be a simple problem; however, it ...
1
vote
1answer
200 views

how to reduce the time to calculate triple integral

i want to evaluate the following integral, but it takes 15 min to do it. i must reduce the time to calculate it, i have to do a table and create a graph, but takes too long. anyone have an idea ? ...
0
votes
1answer
56 views

Is there a more idiomatic way to solve this implicit differentiation problem?

Here's an exercise from a calculus text by Larson and Edwards: Find the rate of change of the distance between the origin and a moving point on the graph of $y = x^2 + 1$ if $dx/dt = 2$ ...
2
votes
0answers
168 views

Derivatives of list elements

Could someone explain the odd behavior of the Derivative function when drawing arguments from lists? We have, ...
0
votes
0answers
33 views

Plot derivative of integral with changing limits [duplicate]

My code is: Plot[D[Integrate[E^(t*(-x^2)),{x,t+2,t^2}],t],{t,-2,3}]. The errors/warnings are: ...
9
votes
0answers
240 views

Why does Mathematica give an incorrect answer to this multiple integral?

This is not a new problem but I would like to understand why Mathematica gives the result that it does. (Volume of a hypersphere) ...
0
votes
1answer
94 views

Simple Question: Derivative of a path

I have a path V[t_]:={3t^2,2,6t}, and I define F[t_]:=V[t]/Norm[V[t]]. I simply want the derivative of ...
2
votes
1answer
769 views

Laurent series expansion

Can someone share how to find a Laurent series expansion of $$f(z)=\frac{1}{(z^2-1)(z^2-4)}$$ centered at zero on the annular disk $1<|z|<2$?
3
votes
2answers
1k views

How do I evaluate a double or triple integral over a region?

Say I need to evaluate the integral $\iiint_W f(x,y,z) dx dy dz$ and $W$ is a region given to me like $W = \{ (x,y,z) : 1 \leq x^2 + y^2 \leq 4, 1 \leq z \leq 5\}$. I don't how to do this with a ...
5
votes
2answers
168 views

Why does Integrate return a solution that is not defined at a particular point when it actually is well defined at that point?

I am trying to compute Integrate[Sqrt[x^4 + (y - y^2)^2], {x, 0, y}] Mathematica 8 gives ...
2
votes
2answers
219 views

integrating slightly complicated expression which includes Abs

I have been waiting for Mathematica to give me something for the following integral, errors welcome, but it has been "running" for almost 30 minutes now. ...
5
votes
2answers
221 views

Mathematica cannot calculate a limit

When I evaluate Limit[E^(-n)*Sum[n^k/(k!),{k,0,n}], n -> ∞] Mathematica gives me the result ...
1
vote
0answers
119 views

Getting poles of a Gamma functions [duplicate]

Why do the following 2 sequences give different answers? n = 1.5 Series[Gamma[0.5 - n - x], {x, 0, 2}] Series[Gamma[-1 - x], {x, 0, 2}] (..clearly the output from the second expression is ...
4
votes
0answers
168 views

Strange result from evaluating a Limit expression

When I evaluate the limit of (1-Cos[x]) Sin[1/x] at x = 0 in Mathematica 9, I obtained ...
8
votes
2answers
333 views

Why does Integrate declare a convergent integral divergent?

When I try this command Integrate[1/Sqrt[(s^2 - u)^2 - 1], {s, m, Infinity}, Assumptions -> u > 2 && m > 10] Mathematica declares that the ...
1
vote
2answers
260 views

Implicit differentiation to find the slope of the tangent line to the graph at the indicated point [duplicate]

I used ContourPlot to plot the graph of x Sin[Pi y] - y Cos[Pi x] == 1 with the following input: ...
-3
votes
1answer
151 views

Limit of a subsequence

I am trying to calculate limit for a subsequence <${ a }_{ {n }^{ 2} }$> because I was trying to see that limits of sequences and subsequences are both same. I was able to generate the sum for ...
3
votes
2answers
264 views

How do I represent a system dynamics feedback loop?

In System Dynamics, if I want represent the relationship between Speed and Distances, I create a Flow (Speed) and a Stock (Distance) as you can see in this Insight Maker Sample . Heres an Image of how ...
4
votes
1answer
697 views

Is it possible to impose “Assumptions” in DSolve or equivalent? (differential equation solving)

When DSolve tries to solve differential equations, it is sometimes not smart enough to generate conditions according to different possible value of parameters. ...
1
vote
1answer
107 views

How to evaluate an integral

I am trying to evaluate this integral Integrate[(kx^2/2)*Sin[\[Lambda]x], x] from -pi/2(lamda) to pi/2(lamda) Everything there is a constant, and the only ...
3
votes
2answers
217 views

Computing the minimum distance in a contour plot

I have the following Mathematica code ...
10
votes
2answers
513 views

Numerical partial derivative

For a one-variable numerical function, it's simple to calculate the derivative at a point with Derivative as Szabolcs has pointed out before: ...
3
votes
1answer
229 views

Sum and NSum gives different solutions

I'm working on a Mathematica lab for Calc. 2, and I ran into a problem last night. I was trying to calculate the midpoint approximation of the definite integral of ...
2
votes
3answers
149 views

Manipulate fails with f[x]=x^k/(1+x^k)

I have: Clear[f] f = Function[x, x^k/(1 + x^k)]; Manipulate[ Plot[f[x], {x, 0, 5}], {k, 1, 10}] But nothing draws as I move the slider. Am I missing something? ...
1
vote
2answers
158 views

Solve f'[x]==0 for x

I tried the following: f[x_] := x^n/(k + x^(2 n)); Solve[f'[x] == 0, x] But I got the following response: Solve::nsmet: This system cannot be solved with the ...
0
votes
2answers
390 views

Using Mathematica to find poles of Gamma functions

I am concerned about the expression on the RHS of equation A.5 (page 19) in this paper: $$\int\frac{d^d ...
9
votes
2answers
441 views

Find closed form expression for series expansion coefficients [duplicate]

Is there a built-in function that will find a general expression for the coefficient of the series expansion of a function? Series will only give the explicit ...
0
votes
1answer
1k views
0
votes
1answer
206 views

Integrating polynomial functions over polytopes with an add-on package

There is a Mathematica package to evaluate integrals over polytopes: http://library.wolfram.com/infocenter/Books/3652/ In the documentation (Functions.nb file) I ...
15
votes
4answers
3k views

Finding Limits in several variables

Is there a way to find a limit of a multivariable function, like $$\lim_{(x,y)\to (0,0)} f(x,y)$$ with Mathematica? When $f$ is continuous, we can use $$\lim_{(x,y)\to (0,0)} ...
2
votes
1answer
326 views

Volterra integral equation : 'literally match the independent variables' message

I want to solve an Volterra type Integral equation, and as a practice I entered the following code to my mathematica: ...
7
votes
2answers
498 views

How to change coordinates of integration?

Is there some built-in routine, some easier method to change variables of integration, without/before solving the integral? Say I have ...
2
votes
3answers
706 views

Multiple assumptions in integral

I want to add two assumptions, so I can get this probability density function to equal 1, though I can't get a solution. ...
0
votes
1answer
200 views

NumericQ prevents evaluation at a numerical value sometimes

I set up a symbolic integral, to be evaluated only when some of the symbols have been replaced by numbers. The evaluation after assigning numbers to the symbols is still symbolic for some reason. The ...
2
votes
1answer
199 views

Integrate[(1 + x/n)^n*Exp[-x], {x, 0, Infinity}]

I evaluated Integrate[(1 + x/n)^n*Exp[-x], {x, 0, Infinity}] . thinking the answer should be approximately $\sqrt{\pi n/2}$. Mathematica gave me ...
5
votes
3answers
266 views

Integration gives ComplexInfinity when it shouldn't

A simple example of my problem is that Assuming[k ∈ Reals, Integrate[Exp[l]/((1 + Exp[l])*Exp[k*l]), l]] /. {k -> 2} gives ...
4
votes
0answers
131 views

Version 8.0 integrates but Version 9.0.1 doesn't

I am trying to run the following integral in version 9.0, but it fails: ...
15
votes
2answers
285 views

Inconsistent results from equivalent integrals

Why is Mathematica returning different values for these two integrals: I am just being introduced to complex integration, so it's possible that I have a misunderstanding of how this works, but in ...
9
votes
4answers
909 views

Plot a 2D vector path onto a surface

In my calculus 3 course, we're studying gradients and have a project that takes a combination of 3D Gaussian radial surfaces and a basic parametric path $r(t) = \{x(t),y(t)\}$ to see how the gradient ...