$\lim\limits_{x\to a}\left(\frac{x^x-a^x}{x^a-a^a}\right)$ using L'Hospital's rule.
55654
Limit of $\frac{x^y-y^x}{x^x-y^y} $ while $x\to y$
135159
Limits using L'Hopital's rule $\lim_{x\to0^+} (x^{x^x-1})$
71891
$\lim_{x \to 0} f(x)=\frac{\tan 3x}{\tan 2x}$ without L'Hospital
33701
Find this limit using L`Hopitals rule
147264
$ (1 + x)^{1/x} $ when $ x \to \infty$ without L’Hospital’s Rule
79618
Find the limit without use of L'Hôpital or Taylor series: $\lim \limits_{x\rightarrow 0} \left(\frac{1}{x^2}-\frac{1}{\sin^2 x}\right)$
103055
Proving the quotient rule for limits
35169
Finding the limit of $\left(\frac{n}{n+1}\right)^n$
40487
Given $\lim_{x \rightarrow a}f(x)+\frac1{\left|f(x)\right|}=0$, what is $\lim_{x \rightarrow a}f(x)$?
111929
Find the limit: $\lim_\limits{x\to 0}{\frac{\left(1+x\right)^{1/x}-e}{x}}$
27717
Compute $\lim_{x\to\infty}x\;\left[\left(1+\frac{1}{x}\right)^x-e\right]$
3619
Proof for $\lim_{n \to \infty}\left(1+\frac{a_n}{n}\right)^n = e^a$?
109907
How to prove that $\lim\limits_{h \to 0} \frac{a^h - 1}{h} = \ln a$
19898
Limit $\lim (1+(a^{1/n}-1) / b)^n$
51622
Evaluating $\lim\limits_{x\rightarrow0}\frac{e^{-1/x^2}}{x}$
106742
Evaluating $ \lim_{x \rightarrow 0}\left (\frac{\sin(x)}{x}\right)^\frac{1}{x^2}$
68891
Are the limits $\lim\limits_{n\to \infty }\left|\frac{a_{n+1}}{a_n}\right|\,$ and $\lim\limits_{n\to \infty }\sqrt[n]{|a_n|}\,$ equal?