New posts in calculus

$f'$ exists, but $\lim \frac{f(x)-f(y)}{x-y}$ does not exist

calculus limits derivatives

Prove that there is no function $f:\Bbb{R}\to\Bbb{R}$ with $f(0)>0$ such that $\forall x,y\in\Bbb{R}, f(x+y)\geq f(x)+y f(f(x))$

calculus real-analysis limits functional-equations

Closed-forms of real parts of special value dilogarithm identities from inverse tangent integral function

calculus special-functions closed-form polylogarithm

Limit of $x^{1/x}$

calculus limits

Why aren't there two equivalent ways to set up the limits of integraion for P(X>Y)?

calculus probability integration statistics multivariable-calculus

Integrate $I(a) = \int_0^{\pi/2} \frac{dx}{1-a\sin x}$

calculus integration trigonometry definite-integrals closed-form

How do I parametrize a circle that's not centered at the origin?

calculus algebra-precalculus geometry multivariable-calculus trigonometry

Evaluating the limit of a certain definite integral

calculus real-analysis integration limits closed-form

A reason for the value of $\int_{0}^{1}\log{(x)}\log{(1-x)}\,\mathrm{d}x$

calculus integration definite-integrals soft-question logarithms

Evaluating $~\int_0^1\sqrt{\frac{1+x^n}{1-x^n}}~dx~$ and $~\int_0^1\sqrt[n]{\frac{1+x^2}{1-x^2}}~dx$

calculus integration definite-integrals closed-form beta-function

another product of log integral

calculus integration definite-integrals

find the maximum possible area of $\triangle{ABC}$

calculus geometry optimization triangles area

When could we get $f' = f^{-1}$, where $f^{-1}$ is the inverse function of $f$, and not $\frac{1}{f}$

calculus ordinary-differential-equations

Evaluation of $\sum^{\infty}_{n=1}\left(\frac{1}{3n+1}-\frac{1}{3n+2}\right)$

Using Rolle's Theorem to prove roots.

calculus derivatives roots rolles-theorem

Integral $\int_{-1}^{1} \frac{1}{(1+u^2)^{n/2}} \exp{\left(-2\pi \frac{a^2+b^2}{1+u^2}\right)} \exp{\left(-4\pi i ab \frac{u}{1+u^2}\right)} du $

calculus integration definite-integrals special-functions complex-integration

Is the tangent function (like in trig) and tangent lines the same?

calculus trigonometry terminology circles

Integral with exp and erf

calculus special-functions definite-integrals

Prove $\frac{1}{a^3+b^3+abc}+\frac{1}{a^3+c^3+abc}+\frac{1}{b^3+c^3+abc} \leq \frac{1}{abc}$

calculus elementary-number-theory arithmetic

Proof for the "Fundamental Calculus Theorem" for two variables.

calculus multivariable-calculus proof-writing