# Tagged Questions

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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### Huge difference after changing a fraction to decimal

I have a limit to calculate. With[{p = 1/2, q = 0.1}, Limit[a^q Integrate[Sin[x]/x^p, {x, a, Infinity}], a -> Infinity]] gives correct result ...
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### Wrong limit involving sine?

Using Mathematica 9.0.0.0, I was trying to calculate the sum $$B_n = \sum_{i=1}^n \sin^4\left(\frac{(i-1)}{(n-1)}\cdot\frac{\pi}{2}\right).$$ where I thought it would be $B_n = \frac{3(n-1) + 4}{8}$....
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### How to perform this nth derivative operation in MMA?

I have to solve this following equation where I need to differentiate a function $n$ times. $$A=\sum_{n=0}^{m-1}\frac{s^n}{n!}(-1)^n\frac{d^nf(s)}{ds^n}$$ How to express the above equation in ...
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### Recycle boundary condition

I'm having the following issue that can not find a solution , by using this boundary condition u[0, t] == 2 u[1, t] that Mathematica does not understand, someone ...
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I noticed a bug in Mathematica. It computes incorrectly a definite integral ...
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### Asymptotic form of the “strange” function

I want to find the asymptotic form of this function ...
94 views

### Integrating the sum gives different answer that summing the integrals of the terms

I wrote this code: ...
We are asked to find $dy/dx$ when $x^y=y^x$. Our hand calculations use logarithmic differentiation. \begin{align*} x^y&=y^x\\ \ln x^y&=\ln y^x\\ y\ln x&=x\ln y\\ \end{align*} Then we ...
Now I have a function, say $f(k,z)=e^{-kz}(1+kz)$ I want to find the $n$th $\log$ derivative with respect to z. like $(z\partial_z)^{(n)}f(k,z)$ (or $(\partial_{\ln z})^{(n)}f(k,z)$ if you like), ...