0
votes
0answers
35 views

Deciding lambda and integrate a function [on hold]

I want to decide lambda for this function I also want to integrate the same function. Please help!
0
votes
1answer
89 views

Evaluate integral of a series

I want to evaluate this integral, but it won't work. Does anyone knows why? ...
0
votes
1answer
41 views

Showing result of derivative and other functions [closed]

I have a problem with my Mathematica 7.0 When I write: Derivative[x^2, x] Mathematica returns as result : ...
1
vote
1answer
105 views

Function derivatives in arbitrary dimension

I have a higher dimensional function: $$f(x,t)=-\ln(t)-\ln(1-\left\|x\right\|^2-t^2)$$ where $x\in\mathbb{R}^n,~t\in\mathbb{R}$. I want to compute the derivatives with the commands ...
4
votes
1answer
127 views

Volume within parameter space

Imagine a parameter space with variable 0<p<1, 0<e1<1/2 and 0<e2<1/2. ...
5
votes
0answers
157 views

Strange Integrate behavior (a bug!)

The following two calculations should give the same result. After all, integration is a linear operation. I have pasted the code below in case you want to play with it. ...
3
votes
1answer
223 views

Integral of Lorentzian yields different results depending on when parameter assigments are made

I'm evaluating the integral of a Lorentzian, which I know equals one. First I define the function and evaluate the integral in two slightly different ways. Surprisingly, I do not get the right answer ...
3
votes
3answers
169 views

What is the formula for this numerical series?

I'm developing a questions game. My goal is that the score for each correct answer will increase as the user answers more questions. Initially there are 15 points for each correct answer. Every 4 ...
14
votes
1answer
271 views

How to represent a continuous monotonic phase of Airy functions?

Note: In this question I am concerned only with real-valued variables and functions. DLMF, §9.8 Airy Functions, Modulus and Phase, formula $9.8.4$ defines the phase of Airy functions: ...
5
votes
2answers
486 views

How to find the non-differentiable point(s) of a given continuous function?

For example, the non-differentiable point of the function $f(x)=|x|$ is at $x=0$. How to find the non-differentiable points of a continuous function that is defined numerically?
1
vote
0answers
141 views

Positive integrand giving negative answer

I'm integrating a positive function f(t) times sin(t) from 0 to pi/5 and get -38. Actually f is slightly negative for a short time (smallest value ~ -0.0005), but far from enough to explain this. ...
6
votes
1answer
226 views

solve ODE with divergencies

The solutions of the second order differential equation $$\frac{1}{\eta}\frac{d}{d\eta}\left(\eta \frac{df}{d\eta}\right)+\left(1-\frac{s^2}{\eta^2}\right)f-f^3=0$$ is shown in Fig. 5.2 below, for ...
2
votes
1answer
388 views

How to take the derivative w.r.t. an arbitrary function?

EDIT: The answer posted by @Jens works for built-in functions only. However I'm starting to wonder if this is related to my Mathematica install somehow. I have version 7. Here is an example in the ...
1
vote
1answer
136 views

Derivative inside a function

I am trying a problem that should be simple: to create a function that contains a derivative. I need to do a more complex example, but even with the simplest I'm having trouble: Let's consider ...
9
votes
1answer
278 views

Is it possible to find a limit of a sequence given by its recurrence relation?

I need to calculate a limit of a sequence given by its recurrence relation. I tried the following: ...
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 ...
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: ...
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
124 views

How can I calculate a limit with a free variable?

For example, when I evaluate Limit[(1 + x^n + (x^2/2)^n)^(1/n), n -> Infinity] Mathematica does not output any result. When I evaluate ...
0
votes
0answers
108 views

Strange result from integrate

I am working on the following problem. However, the first task takes too long, although the answer 0 is correct. In the second task, to reduce the calculation time, ...
0
votes
1answer
930 views

Given x[u,v], y[u,v], and f[x,y] how do I find D[f,x] in terms of u,v?

I have two functions x = x(u,v) and y = y(u,v). The chain rule says that for a function f(x,y), df/dx = df/du du/dx + df/dv dv/dx, and similarly df/dy = df/du du/dy + df/dv dv/dy. How do I get ...
0
votes
1answer
392 views

Evaluate multivariable function [closed]

I'm trying to use Mathematica to evaluate many values of $f(x,y) $, like $f(-\pi,\pi) $ for $$f(x,y) = \left( \frac{-1}{4}\sin \left( \frac{x-y}{2} \right)\sin y \right)\left( \frac{-5}{4}\sin ...
4
votes
3answers
2k views

How can I differentiate Numerically?

Mathematica has two ways to integrate: Integrate and NIntegrate. But what about D? ...
2
votes
1answer
243 views

About high dimensional integrals

I want to be able to do high dimensional integrals like, (..naively I wrote it as this..) ...
8
votes
1answer
282 views

ReplaceAll[] and Limit[] don't give correct results for this expression under extreme variables [duplicate]

Possible Duplicate: Funny behaviour when plotting a polynomial of high degree and large coefficients 1/x^2 + (3 + x)/(6 (1 - Exp[x] + x)) ——This is a ...
1
vote
1answer
113 views

How to explain the results of the following integrals?

Why does the following program lead to different results of a21 and a211? ...
11
votes
4answers
4k views

How to find the domain and range of a function with Mathematica?

I'm studying calculus and in some exercises I am asked to find the domain and range of a function. Does Mathematica have already a built-in function for this? I can imagine some ways of doing so, ...
7
votes
3answers
481 views

Inverting a function in a certain region

InverseFunction works well for globally invertible functions, like f = 2*# + 2 &; InverseFunction[f] ...