Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.
10
votes
2answers
173 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
94 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.
...
5
votes
4answers
178 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 ...
1
vote
2answers
143 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
67 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
77 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
73 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
71 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 ...
1
vote
2answers
73 views
6
votes
1answer
83 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.
...
7
votes
1answer
122 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
113 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
101 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
39 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
89 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
30 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:
...
8
votes
0answers
125 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
53 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
2answers
179 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
135 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
147 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
110 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
69 views
Getting poles of a Gamma functions
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
116 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 ...
6
votes
2answers
150 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
112 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:
...
1
vote
0answers
118 views
Why won't Mathematica integrate this? [closed]
I have absolutely no programming knowledge but my college requires us to use Mathematica in our calculus classes. This is the first time I've ever had to do any work without a partner and I've gotten ...
-3
votes
1answer
101 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
147 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 ...
2
votes
1answer
125 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
68 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
135 views
6
votes
2answers
213 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:
...
0
votes
0answers
109 views
Integrating the product of two modified Bessel functions of the second kind [closed]
I want to integrate the product of two modified Bessel functions of the second kind, as follows:
...
1
vote
1answer
113 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
121 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
138 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
197 views
Using Mathematica to find poles of Gamma functions [closed]
I am concerned about the expression on the RHS of equation A.5 (page 19) in this paper:
$$\int\frac{d^d ...
0
votes
0answers
115 views
Inspecting a function around a singularity [closed]
I am plotting a function which is defined as the ratio between an interpolating function (the solution of some integral equation) and $x^2$, so something like $g(x)=f(x)/x^2$. From the plot of $f(x)$, ...
9
votes
2answers
204 views
Find closed form expression for series expansion coefficients [duplicate]
Is there a built-in function that will find a general expression for the coefficient of the series expansion of a function?
Series will only give the explicit ...
0
votes
1answer
126 views
0
votes
1answer
77 views
Integrating polynomial functions over polytopes with an add-on package
There is a Mathematica package to evaluate integrals over polytopes:
http://library.wolfram.com/infocenter/Books/3652/
In the documentation (Functions.nb file) I ...
14
votes
4answers
465 views
Finding Limits in several variables
Is there a way to find a limit of a multivariable function, like
$$\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
156 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
137 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
127 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
0answers
65 views
Complex Integration Optimization
The following code culminates in plots calculated for each value of t as given below.
I have tried compiling one of the functions and adjusting the precision of both the integration and the plotting ...
0
votes
1answer
83 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
130 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
151 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 ...
