Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.
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?
...
3
votes
1answer
92 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
177 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 ...
14
votes
4answers
457 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
$$\lim_{(x,y)\to (0,0)} ...
6
votes
1answer
341 views
How to expand a function into a power series with negative powers?
Is there any way to expand this expression
a+b(1-Exp[-T/(b c)]/(z-Exp[-T/ (b c)])
(where a, ...
1
vote
2answers
139 views
Write a function that returns the logarithmic derivative
How can we write a function that if we input an expression f, it returns the log derivative $\frac{1}{f} \frac{df}{dx}$. We have to use a conditional or pattern test so that the function accepts any ...
3
votes
1answer
390 views
Definite and Indefinite integral give different results for piecewise function
I have the following function:
$$
f(q,y)=
\begin{cases}
\tfrac{11720+p}{37791360} & -11720<p<-7720 \\
0 & \text{True}
\end{cases}
$$
where $p = 443\ y-777600\ \sin^{-1}\left(\frac{q ...
1
vote
1answer
67 views
Integration of a rational function
I am trying to solve the following rational integral (I got assistance here):
$$\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
67 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 ...
8
votes
5answers
1k views
Finding the centroid of the area between two curves
When I have an area bounded by curves, is there a built-in way to find the center of the area? Or do I have to plot it first and then use ComponentMeasurements on ...
6
votes
3answers
964 views
How to find the nth derivative?
This question is not the same as my last one. How do you find the $n$-th derivative where $n$ is a variable?
For example, you can find the nth derivative for a specific $n = 3$
...
9
votes
2answers
285 views
Derivative from the left and right
I am currently trying to write a script that takes a curve $C$, a starting point $p$ and a direction vector $\vec{v}$ and calculates the path of a beam starting at $p$ in direction $\vec{v}$ when it ...
1
vote
3answers
244 views
How do I evaluate several n-th derivatives of a function at one point?
I have a question where I have to compute a Table containing $f^{(n)}(0)$ for n = 1, ..., 5, where $f^{(n)}$ denotes the $n$th ...
9
votes
2answers
202 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 ...
1
vote
2answers
73 views
5
votes
1answer
79 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
117 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:
...
2
votes
1answer
123 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. ...
4
votes
2answers
112 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 ?
...
1
vote
1answer
100 views
Assumptions are not being applied to integral
I am trying to use assumptions to simplify an integral, but I can't seem to get the assumptions to apply themselves. Here is the code I am using:
Note the expressions in the assumption can be found ...
0
votes
2answers
393 views
About generating power series
For an arbitrary function $f(x,y)$ I am defining functions LogMT1 and LogMT2 as follows,
...
0
votes
1answer
38 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 $dx/dt = 2$ ...
6
votes
2answers
210 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:
...
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:
...
1
vote
0answers
151 views
Function approaching incorrect limit in mathematica [closed]
I am interested in the complex function
$f(z)=\frac{1}{a}\log\left[2\sinh(a\sqrt{z})\right]$.
where $a > 0$ is a real parameter. Clearly for large $a$ this approaches $f(z) \to \sqrt{z}$.
But ...
8
votes
0answers
123 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)
...
2
votes
1answer
155 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:
...
3
votes
3answers
402 views
Definite integral takes a very long time
I'm trying to integrate the following function:
$$
r_e=\int_0^z\frac{dz}{\sqrt{\Omega_m(1+z)^3+\Omega_\Lambda}}
$$
where $\Omega_\Lambda=1-\Omega_M$ and both $\Omega_\Lambda$ and $\Omega_M$ are real ...
2
votes
2answers
176 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 ...
0
votes
1answer
50 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
146 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.
...
7
votes
2answers
136 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
...
3
votes
3answers
219 views
Proving a recurrence in Mathematica
I have
$$j_n=\int_0^1 x^{2n} \sin(\pi x)dx.$$
How do I show that $$j_{n+1}= \frac{1}{\pi^2}(\pi- (2n+1)(2n+2)j_n)\, ?$$
I keep getting a recurring integration by parts and I can't simplify it.
...
5
votes
2answers
134 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
...
6
votes
5answers
561 views
Trying to prove that $x\sin(\frac{\pi}{x})\ge\pi \cos(\frac{\pi}{x})$ for $x\ge 1$
Consider the function
f[x_] := x Sin[Pi/x]
I want to prove that this function is increasing for $x\ge 1$. This can be done with the first derivative. We have to ...
4
votes
0answers
115 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 ...
5
votes
2answers
108 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
...
0
votes
1answer
751 views
Quick Hessian matrix and gradient calculation?
I am absolutely new to Mathematica and I actually want to try implementing a little optimization method .
Long story short assuming I have a predefined two-variable function f(x,y) I want to ...
6
votes
2answers
146 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 ...
-3
votes
1answer
99 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 ...
1
vote
0answers
68 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 ...
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 ...
1
vote
2answers
110 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:
...
15
votes
1answer
287 views
Speeding up trigonometric integral
Context
On a possible non trivial toric topology for the Universe (nothing less!).
Problem
I would like to carry out the following integral for $\ell=2,4\cdots 20$.
$$\int _0^{\pi }\int _0^{2 \pi ...
21
votes
3answers
1k views
How to find the period of an arbitrary mathematical function?
Is there a function to find the period of an arbitrary (possibly complex) function in Mathematica?
3
votes
2answers
144 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 ...
