Questions related to the calculus and analysis branches of Mathematica, including, but not limited to, limits, derivatives, integrals, series, and residues.
0
votes
0answers
9 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
78 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
28 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:
...
5
votes
0answers
101 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
37 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
145 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
132 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
...
-1
votes
0answers
64 views
Small bug or my mistake (solve one integral)? [closed]
Why Mathemathica 9 solve this Integral Integrate[1/(x^3 - 1), x] wrong?
...
2
votes
2answers
137 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.
...
0
votes
0answers
43 views
Integration solving [duplicate]
A integration is given $$x-x_0 = \pm \int_{x_0}^{x}\frac{d\Phi}{\frac{\lambda}{2}(\Phi^2-\frac{m^2}{\lambda})}$$
the solution of this integration is given,
$$\Phi(x)= \pm \left(\frac{m}{\sqrt\lambda ...
5
votes
2answers
101 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
0answers
58 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
111 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
111 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
78 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:
...
0
votes
0answers
116 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
93 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
123 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 ...
1
vote
1answer
83 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
62 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
131 views
6
votes
2answers
172 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
1answer
132 views
0
votes
0answers
91 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
108 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 ...
1
vote
2answers
80 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
134 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
178 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:
$$\int\frac{d^d ...
0
votes
0answers
113 views
Inspecting a function around a singularity [closed]
I am plotting a function which is defined as the ratio between an interpolating function (the solution of some integral equation) and $x^2$, so something like $g(x)=f(x)/x^2$. From the plot of $f(x)$, ...
0
votes
1answer
68 views
0
votes
1answer
62 views
Integrating polynomial functions over polytopes with an add-on package
There is a Mathematica package to evaluate integrals over polytopes:
http://library.wolfram.com/infocenter/Books/3652/
In the documentation (Functions.nb file) I ...
13
votes
4answers
350 views
Finding Limits in several variables
Is there a way to find a limit of a multivariable function, such like
$$\lim_{(x,y)\to (0,0)} f(x,y)$$
with Mathematica?
When $f$ is continuous we can use that
$$\lim_{(x,y)\to (0,0)} ...
2
votes
1answer
139 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
133 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
112 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
59 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
70 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
108 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
136 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
108 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
201 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 ...
8
votes
4answers
381 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 ...
4
votes
4answers
190 views
Differentiating space curves
I'm trying to do some very basic differential geometry of space curves. For example, a space curve $\gamma:\mathbb R\to\mathbb R^3$ has unit tangent and normal vectors given by
...
3
votes
1answer
86 views
Why is the output of my limit expression an interval?
Why is the output of the limit below an interval? It should be precisely $1$.
...
1
vote
0answers
56 views
Symbolic Integration of Boole [closed]
Why is
Integrate[Boole[x < 1], q]
resulting in
Piecewise[{{x, x <= 1}}, 1]
I'd expect
...
5
votes
1answer
95 views
Definite Integral over a path
What does
Integrate[f[z], {z, a, b, c, d}]
exactly calculate? Is it
$$\int_a^b f(z)\, \mathrm{d}z +\int_b^c f(z)\, \mathrm{d}z
+\int_{c}^d f(z)\, \mathrm{d}z ...
0
votes
1answer
78 views
Integrate function without specifying limits of integration
I've been having trouble to make mathematica evaluate an integral without specifying the values of the limits of integration. I mean, if I write
...
1
vote
1answer
163 views
0
votes
1answer
156 views
No output for N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]]
Is my input below correct? I've received no response from Mathematica.
N[Limit[Integrate[Sin[x]^n/(Sin[x]^n + Cos[x]^n), {x, 0, Pi/2}], n -> Infinity]]
Thank ...
1
vote
2answers
238 views
3N-dimensional integral
I'm trying to compute a multidimensional integral with a variable number of dimensions.
The integral is as follows:
$$
\int d^{3N}\!p~e^{-\frac{\beta}{2m}\vec p^2}.
$$
I have tried this
...
