# Questions tagged [calculus-and-analysis]

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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### Finding a function that has no minimum

I started looking for a non-negative function that has no minimum. I used the necessary condition for an extremum with partial derivatives, but the found functions still did not satisfy the condition ...
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### I have a list of coefficients and I am trying to make a power series. How?

I noticed the Series[] command that would be perfect for Taylor polynomials. Unfortunately, I do not have the function available. I just have a list with the ...
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### Double integral with a variable in limits

I am trying to solve this integral: This is what I tried: ...
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### Evaluating a 2d integral

I would like to calculate this integral \begin{align*} I(s_1,s_2,s_{12},m) = \int_{0}^{1} {\rm d}x \int_{0}^{1-x} {\rm d}y \Big( x y \Big[ y(1-y)s_1 + x(1-x)s_2 + 2 xy s_{12} -m^2 \Big]^{-1} \Big), \...
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### How to perform brute force method with Knapsack /0-1 money-changing problem, with the following table of potential knapsack items

This is the listing item with 400 as Knapsack size... ...
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### How to show the resulting function hidden by Mathematica?

I have u0[r_, phi_] := Sum[I^(-n) BesselJ[n, r] Exp[I n phi], {n, -n, n}]; Limit[u0[r, phi], n -> Infinity] but the result is not exportable to TEX, as it is ...
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### Heuristics, tricks, and hacks in symbolic math

Mathematica sometimes fails to compute symbolic solutions when posed in the direct or obvious code, but succeeds when the same fundamental problem is posed in a slightly different way, or when ...
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### Why can't Mathematica integrate my function?

I am very new to Mathematica and have been trying to integrate a function p[f] that is expressed as follows ...
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### How to integrate faster

I always wanted to know how to speed up my integral computation in Mathematica. Is there some techniques that i am unaware to make the integration faster. Here an example: ...