New posts in calculus

Convergence of a series (quite frustrating)

calculus sequences-and-series

Evaluation of $\int_{0}^{\frac{\pi}{2}}\frac{\sin (2015x)}{\sin x+\cos x}dx$

calculus definite-integrals

Let $a_n>0$ be bounded and: $\displaystyle\limsup_{n\to\infty}\frac 1 {a_n}=\frac 1 {\displaystyle\liminf_{n\to\infty}a_n}$ [duplicate]

calculus sequences-and-series inequality proof-verification limsup-and-liminf

Can I interpret the exponential of the derivative operator, $e^D$, as infinite shift operators each shifting "infinitesimally"?

calculus derivatives exponential-function

Taylor series not converging, other example than $\exp(-1/x^2)$?

calculus real-analysis convergence-divergence taylor-expansion

Can we find a function $f:\mathbb{R}\rightarrow \mathbb{R}$ that is open, closed, but not continuous?

calculus real-analysis reference-request

How do I evaluate this definite integral?

calculus integration functions definite-integrals

Convergence of the function series $\sum _{n=1}^{\infty}\dfrac{(nx)^n}{n!}$ [duplicate]

calculus sequences-and-series

Finding parametric curves on a sphere

calculus differential-geometry

Double Integral $\int\limits_0^a\int\limits_0^a\frac{dx\,dy}{(x^2+y^2+a^2)^\frac32}$

calculus integration multivariable-calculus definite-integrals multiple-integral

How do we know the Taylor expansion for $e^x$ works for all $x$? Or that it's analytic?

calculus sequences-and-series taylor-expansion exponential-function analytic-functions

Proving roots with Mean Value Theorem [closed]

calculus

limit of the sequence $a_n=1+\frac{1}{a_{n-1}}$ and $a_1=1$

calculus real-analysis sequences-and-series convergence-divergence recurrence-relations

How to prove this inequality about the arc-length of convex functions?

calculus definite-integrals convex-analysis plane-curves

How come $\lim_{x\to0}$ $x^x = 1$?

calculus limits

Solution of an ODE in sections

calculus ordinary-differential-equations

Why are the coefficients of the equation of a plane the normal vector of a plane?

calculus multivariable-calculus vectors plane-geometry

What is $ \lim_{n\to\infty}\frac{1}{e^n}\Bigl(1+\frac1n\Bigr)^{n^2}$?

calculus sequences-and-series limits convergence-divergence exponential-function

Can you reduce an inequality by taking a derivative?

calculus algebra-precalculus

Is my general formula for polynomial multiplication right?

calculus algebra-precalculus