Newbetuts

Why does $ \frac{2x}{2+x}$ provide a particularly tight lower bound for $\ln(1+x)$ for small positive values of $x$?

Probabilistic techniques, methods, and ideas in ("undergraduate") real analysis

Substitution for definite integrals

A theorem about Cesàro mean, related to Stolz-Cesàro theorem

If $h$ is twice differentiable, then $|h|$ is twice differentiable except on a countable set

What's the geometrical interpretation of the magnitude of gradient generally?

Convergence tests for improper multiple integrals

Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$

PDF of the difference between two independent beta random variables

Help figuring a formula for my job

Volumes of cones, spheres, and cylinders

In deriving the catenary equation, how does integrating $\frac{dy'}{\sqrt{1+(y')^2}}=\frac1a dx$ yield $\sinh^{-1}(y')=\frac{x}{a}$?

Power series for differential equation

Suppose $a_n \ge 0$ for all n and that $\sum_{n=1}^{\infty} (a_n)^2$ converges, does the $\sum_{n=1}^{\infty} a_n$ also converge?

How to find finite trigonometric products [closed]

Prove $\left(\frac{n+1}{\text{e}}\right)^n<n!<\text{e}\left(\frac{n+1}{\text{e}}\right)^{n+1}$ [closed]

New posts in calculus

just for fun integrate $\int \frac{1}{x^2+1}dx$ using Partial Fraction Decomposition

Is there a function such that $f' = f\circ f$?

How to bound this integral?

Where did the negative answer come from in the continued fraction $1+\frac{1}{1+1/(1+\dots)}$?

Why does $ \frac{2x}{2+x}$ provide a particularly tight lower bound for $\ln(1+x)$ for small positive values of $x$?

Probabilistic techniques, methods, and ideas in ("undergraduate") real analysis

Substitution for definite integrals

A theorem about Cesàro mean, related to Stolz-Cesàro theorem

If $h$ is twice differentiable, then $|h|$ is twice differentiable except on a countable set

What's the geometrical interpretation of the magnitude of gradient generally?

Convergence tests for improper multiple integrals

Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$

PDF of the difference between two independent beta random variables

Help figuring a formula for my job

Volumes of cones, spheres, and cylinders

In deriving the catenary equation, how does integrating $\frac{dy'}{\sqrt{1+(y')^2}}=\frac1a dx$ yield $\sinh^{-1}(y')=\frac{x}{a}$?

Power series for differential equation

Suppose $a_n \ge 0$ for all n and that $\sum_{n=1}^{\infty} (a_n)^2$ converges, does the $\sum_{n=1}^{\infty} a_n$ also converge?

How to find finite trigonometric products [closed]

Prove $\left(\frac{n+1}{\text{e}}\right)^n<n!<\text{e}\left(\frac{n+1}{\text{e}}\right)^{n+1}$ [closed]