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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4
votes
1answer
103 views

Finding Euler spiral convergence point for powers other than 2

I'm playing around with Euler spirals, using a variable power to see how the plot changes, $ \left\{\begin{matrix} x = \int_0^s \cos \left ( s^n \right ) ds \\ y = \int_0^s \sin \left ( s^n \right ) ...
1
vote
1answer
67 views

Wrong Limit[…] for inexact expressions

I noticed that Limit can return nonsense when using inexact parameters. In the following code, a is my (exact/inexact) ...
2
votes
2answers
130 views

A simple question: Input problem

I have a simple problem. First I define the value of variables, then I calculate the expression as the following: Code 1: ...
1
vote
2answers
118 views

How to get the $0$ result for this limit?

Consider the following series: $$\sigma (\text{x$\_$})\text{:=}\sqrt{\sum _{k=0}^{x-1} \frac{(x! x!) (-1)^{x-k}}{(x-k) (k! (2 x-k)!)}+\frac{\pi ^2}{12}}$$ From the following codes, it seems that the ...
0
votes
0answers
31 views

How do I numerically integrate the result of NDSolve if it depends on several variables?

I am trying to numerically integrate solution of NDSolve. I am trying to integrate my result of NDsolve in line 97 of my notebook, but am getting the error ...
1
vote
1answer
70 views

The assumption in integration does not work?

I am new to mathematica. Here is the question. I try to do the following integration with the assumption that k1<0, k2<0 and k1,k2 are real number. However, the result includes \sqrt{k1}? ...
4
votes
1answer
89 views

Pertubation series of given equations

I would like to define a function that does the following. If I have an equation, for example: $$f(x)+[1-f^2(x)]+f^{\prime\prime}(x)+f(x)\ f^\prime(x)=0$$ and I am given a value for $f$ to expand ...
0
votes
0answers
16 views

Integration with IntervalMemberQ

I define an interval and its associated index function. ...
0
votes
1answer
71 views

Integrate over FindRoot solutions

I have a function of bivariate normal PDF and its marginals defined as ...
1
vote
1answer
178 views

Derivative of a symbolic matrix

I need to write an elasticity equations as: {{a*∂/∂x,b*∂/∂y},{c*∂/∂x,d*∂/∂y},{e*∂/∂y,f*∂/∂x}}.{{u},{v}} where a,b,...,f are ...
0
votes
2answers
74 views

Expression which should be real-valued appears to be complex-valued [closed]

I want to plot the answer of the following integral: Λ = 10; Ω = 10; t = 1; Integrate[ω E^(-ω/Λ) Sin[(ω + Ω)t/2]^2/(ω + Ω)^2, {ω , 0, ∞}] The answer of ...
2
votes
2answers
138 views

Confirmation of a nice closed form

Can Mathematica 10 confirm a nice closed form for ...
-1
votes
2answers
90 views

Gradient of interpolated 3D data in mathematica 9

tt = Flatten[Table[{x, y, z, btot[x, y, z]}, {x, -1, 1, 0.1}, {y, -1, 1,0.1}, {z, -1, 1, 0.1}], 2]; ff = Interpolation[tt] Till here it is working fine as it is ...
0
votes
2answers
169 views

How can I solve this integral analytically?

I want to solve the following integral: Integrate[( E^(-ω/Λ) Sin[((ω + Ω) t)/2] Sin[(ω t)/ 2])/((ω + Ω)/4) , {ω, 0, ∞}] But unfortunately Mathematica cannot ...
3
votes
0answers
108 views

Why Can't Mathematica Integrate this? [closed]

I am trying to integrate Absolute-value functions from Wikipedia: ...
5
votes
4answers
243 views

Results in terms of a function

Let's assume I have a function $f(x)=\exp(10x^2)$, i.e. f[x_]:= Exp[10*x^2]. When I differentiate $f$ by evaluating the expression ...
1
vote
1answer
130 views

Differential Equations and Unit Notation

What do I get the Syntax::sntxi: Incomplete expression; more input is needed . error when I try to use the math palette for derivatives? What does the dot in ...
3
votes
2answers
195 views

Use Meijer-G function to represent elementary functions

I want to represent these elementary functions: $x^{2}\sqrt{x}$, $\sin{4x}$, and $x\ln{x}$ as cases of MeijerG. What arguments should I give to ...
-1
votes
1answer
63 views

Taylor and Maclaurin series [closed]

I need to calculate limit of sin(x)*cot(tanx) at 0 using Maclaurin series I took the usual approach but did not get anything of help.
3
votes
3answers
210 views

Limit n->Infinity of recursive sequence

I have defined a recursive sequence a[0] := 1 a[n_] := Sqrt[3] + 1/2 a[n - 1] because I want to calculate the Limit for this ...
5
votes
5answers
162 views

How to find the derivative value at $(\pi,0)$ for this implicit function $n$ times?

I am trying to take the implicit derivative at $\sin(x+y)+\sin(x)=y$ and substitute $x=\pi$ and $y=0$ at least 6-7 times since I need to find the Taylor series for this function. Since I barely ...
0
votes
0answers
78 views

How to evaluate this integral

I am trying to evaluate the following integral in Mathematica: ...
0
votes
1answer
54 views

Same integral gives different results with assumption

b = 1 k = 12560 r = 500 res = Integrate[Exp[I*k*x*Sin[o]]/(r + x*Sin[o]), {x, -b/2, b/2}] resab = Abs[res]^2 Plot[resab, {o, -Pi/20, Pi/20}, PlotRange -> Full] ...
1
vote
1answer
121 views

DensityPlot showing artifacts [closed]

This is my first post on Mathematica.SE, and I'm still a bit new to Mathematica. I believe I'm probably doing something silly in my code, but I have not been able to find where. I'm trying to plot a ...
3
votes
0answers
89 views

Inconsistent results for symbolic trigonometric integral

I am trying to evaluate (on Mathematica v.9) the integral \begin{equation} \int_0^x [\sin (x) \sin (2 y)-\sin (2 x) \sin (y)]^t \,\mathrm{d}y, \end{equation} where $t$ is an even, positive integer. ...
3
votes
0answers
94 views

Bug or feature? If statement inside double integrals

(taken from http://math.stackexchange.com/questions/1592901/bug-or-feature-if-statement-inside-double-integrals) Generally speaking, $$ \int_c^a f(x) dx = \int_c^{a-b} f(x) dx + \int_{a-b}^a f(x) ...
5
votes
1answer
101 views

Somewhat Irreproducible Integrate Results

Backslide introduced in v10 and persisting through v10.3.1. In the course of considering question 102922, I encountered erratic results from a particular integration. It is illustrated as follows. ...
5
votes
1answer
74 views

Behavior of D and Derivative when acting on functions with Rules as arguments

I was (pleasantly) surprised that when a Derivative is taken of a symbolic function for which the last few arguments are Rules, ...
2
votes
1answer
98 views

Limit $\sqrt{3-x}$ as $x\to3^+$ [closed]

I'm trying: $$\lim_{x\to3^+}\sqrt{3-x}$$ Using real numbers, technically this limit does not exist. However, Limit[f[x], x -> 3, Direction -> -1] I also ...
5
votes
2answers
155 views

Symbolic integration of SphericalBesselJ

Backslide introduced in v10 and persisting through v10.3.1. Consider the following integral ...
0
votes
1answer
93 views

Integrating the derivative of a function does not give expected result [closed]

I was trying to do the following integral: f[z_]:=Hypergeometric2F1[1,-a,1-a,1/(1-z)]/((1-z)^a-1) Integrate[D[f[z],z],z] I thought the result should be ...
8
votes
2answers
250 views

Can your Mathematica do the following integral?

Backslide introduced in v10 and persisting through v10.3.1. I was trying to do the following integral in Mathematica: ...
4
votes
0answers
106 views

Exploring formal limit definition

I found a few demonstrations on the Wolfram Demonstration Project site that help users to explore the formal definition of a limit. That is, $$\lim_{x\to a}f(x)=L$$ if and only if for every ...
8
votes
1answer
272 views

Strange bug: Product[1/(1-1/2^(n-1)),{n,2,Infinity}] = 0?

This infinite product is correct: Product[1/(1 - 1/2^n), {n, 1, Infinity}] (* 1/QPochhammer[1/2, 1/2] *) Numerical value of this result is not equal to zero ...
-1
votes
2answers
59 views

computing a limit [closed]

I couldn't compute this limit: it should be -3. I couldn't find the analytic way to compute it.
4
votes
1answer
104 views

Parametric numerical integration [closed]

I would like to solve the integral: $$ \iiint\frac{e^{-\sqrt{x^2 + k^2}}x^2 \sin{\theta}}{\sqrt{x^2 + k^2}} dx d\theta d\phi$$ defined in $x \in [0,+\infty]$, $\theta \in [0,\pi]$, $\phi \in [0,2 ...
3
votes
1answer
82 views

Newbie Problem with integral

when I type Integrate[Sign[x], x] to Mathematica, the answer is ∫Sign[x] dx so nothing new. When I type the same to Wolfram ...
1
vote
0answers
119 views

How do I calculate this integral along a complex line (not a contour) in mathematica?

Given the function: $$f(z) = \frac{\pi ^2 \cot(\pi \sqrt z) \cot(\pi \sqrt {z-a})}{4\sqrt{z^2 - az}}$$ Where a is a positive constant and: $$z = \frac{i}{b} + t $$ $$t>a$$ Where b is also a ...
3
votes
2answers
106 views

Correct behavior of Integrate involving logarithmic cut, or possible bug?

I just discovered that Integrate with simple poles in its integrand sometimes gives different results depending on number type of its limit (Exact vs Inexact). ...
0
votes
0answers
84 views

Mathematica: Derivative appears to be wrong

I'm first getting f(x) by computing an implicit equation. Then I want to take the derivative. Later on, when I plot both f(x) ...
3
votes
3answers
271 views

Computing the area between two curves

I want to find the area in between the two curves whenever they overlap each other. I've tried multiple different formulas but none of them have been working. I have to find it using the ...
10
votes
2answers
221 views

Demonstrating the behavior of a function as its independent variable approaches zero

I have several questions regarding the function $$f(x)=\frac{\sqrt{x^2+9}-3}{x^2}$$ that I would like to help my students with in the upcoming semester. Now, the limit as $x\to 0$ is 1/6. ...
5
votes
2answers
214 views

RegionPlot of ImplicitRegion is incorrect

Bug fixed in 10.4. Why does RegionPlot of the ImplicitRegion give an incorrect plot? Also, will how does this affect ...
2
votes
1answer
64 views

Using a grid table to estimate a limit

Consider finding the limit of $f(x)=(x^2-4)/(x-2)$ as $x\to 2$. f[x_] := (x^2 - 4)/(x - 2); I'm looking for some easy ways for my Calc I students (next semester) ...
0
votes
0answers
131 views

Error Message: Invalid integration variable or limit(s) in 1

I write the line: Integrate[1/{1 + Sin[2 x]}, x] And gives the error message: Invalid integration variable or limit(s) in 1. No solutions I'm trying work, and other integration problems are working ...
6
votes
3answers
829 views

Why does Mathematica spit this back out?

I'm struggling with the integral, $$\iint\sqrt{4a^2-x^2-y^2}dxdy$$ taken over the upper half disk of radius a centered at (a, 0). When I type it into Mathematica (10.2), Mathematica spits it back ...
1
vote
0answers
43 views

When evaluating this integral Mathematica returns two different answers

When evaluating this integral in Mathematica 10.3 Student Edition: ...
1
vote
1answer
104 views

Evaluate a double integral over a region [duplicate]

How can I evaluate a double integral over a region in Mathematica? For example $\qquad \iint(x^4+y^2)\,dx\,dy$ for the bounded region $y=x^2$ and $y=x^3$
9
votes
1answer
136 views

Non-rectilinear integration of InterpolatingFunction

Bug introduced in 7 or earlier and persisting through 10.3.1 [CASE:3487737] I have a 2-d array that I would like to resample into a different coordinate system and integrate along one of the new ...
1
vote
1answer
84 views

Integrating sinc function over discontinuity

I would like to analytically integrate the sinc function. First of all, if I just perform the integration the following way, everything is as expected: ...