New posts in Limits

$\lfloor\frac12+\frac1{2^2}+\frac1{2^3}+\cdots\rfloor\;$ vs $\;\lim_{n\to\infty}\lfloor\frac12+\frac1{2^2}+\cdots+\frac1{2^n}\rfloor$

Find $\lim_{x\to 0^{+}} \frac{\theta(x)}{x}$

verifying $\lim\limits_{x \to \infty} (1+\frac{1}{\sqrt{x}})^x$

A property of the function $\frac{\sin x}{x}$

Show that $\lim_{x\to 0^+} xf'(x)=0$.

If the difference quotient $\frac{f(y)-f(x)}{y-x}$ has a limit along a line $(x,y)\to(c,c)$, does the ordinary derivative $f'(c)$ exist?

How to calculate $\lim _{x\to \infty }\left(\frac{x^2+3x+2}{x^2\:-x\:+\:1\:}\right)^x$

What does it mean to converge to a point if it is not clear what the point even is?

L'Hopital's rule conditions

Evaluate $\lim\limits_{n \to \infty}\frac{(-1)^n}{n!}\int_0^n (x-1)(x-2)\cdots(x-n){\rm d}x$