$\mathop{\lim}\limits_{x\to+\infty} \dfrac{\ln x}{x^\varepsilon}, \varepsilon>0$ without L'Hospital's rule
127105
Determining a tricky limit
44060
If $\lim_{x \to +\infty} f'(x) = L$, then $\lim_{x \to \infty} \frac {f(x)}{x} = L$
155979
$\lim_{x\to 0} \frac{\sin x - x}{x^2}$ without L'Hospital or Taylor
147514
How to calculate $\lim \limits_{n \to \infty}(1 +\frac{a}{n})^n$?
74204
Evaluate $\lim_{n\to\infty}(1+x)(1+x^2)\cdots(1+x^{2n}),|x|<1$
144422
How to prove that $\lim\limits_{x\to\infty} f(x)/x=L$
47606
Proving $\lim_{n\to\infty} a^{\frac{1}{n}}=1$ by definition of limit
37489
Show that $ \lim_{(x,y) \to 0} \frac {|x|^ \alpha |y|^ \beta} {|x|^ \gamma + |y|^ \delta} \text {exists} \iff \alpha/\gamma + \beta/\delta > 1.$
146529
Finding the limit $ \lim_{x\to a^+} \frac{\cos(x)\ln(x-a)}{\ln(e^x-e^a)} $
89251
Limit $\lim\limits_{x\to0}{\frac{\ln{(e+x)}-e^x}{\cos^2{x} -e^x}}$
144403
Limit $\lim_{x\rightarrow +\infty}\sqrt{x}e^{-x}\left(\sum_{k=1}^{\infty}\frac{x^{k}}{k!\sqrt{k}}\right)$
138169
Finding $\lim\limits_{n \to \infty }n\int_{0}^{1}\frac{x^{n}}{1+x+x^{n}}dx$
37755
Limit $\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}$
119145
$\lim\limits_{n\rightarrow\infty} \sqrt{n}(\sqrt{n+1}-\sqrt{n})$
4289
$\lim_{x\to0}\dfrac{1}{x}-\lim_{x\to0}\dfrac{1}{x}$
6620
If $\lim\limits_{x\rightarrow\infty} (f'(x)+f(x)) =L<\infty$, does $\lim\limits_{x\rightarrow\infty} f(x) $ exist?
65213
How to find $\lim\limits_{x\to0}\frac{e^x-1-x}{x^2}$ without using l'Hopital's rule nor any series expansion?