Is $\lim_\limits{x\to a}{[f(x)]^{g(x)}}=e^{\lim_\limits{x\to a}{[f(x)-1]·[g(x)]}}$?
95962
proving a theorem from limit using Hopital rule
94564
If $f$ is bounded and $\lim_{x \to c} g(x) = 0$, then $\lim_{x \to c}g(x)f(x) = 0$
30181
Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
73812
Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
104391
Find $\lim_\limits{x\to 1^-}{\ln x\cdot \ln(1-x)}$.
138930
What does $\lim\limits_{x \to \infty} f(x) = 1$ say about $\lim\limits_{x \to \infty} f'(x)$?
26424
If $f(x)<g(x)$ prove that $\lim f(x)<\lim g(x)$
46101
If $f(x)$ is continuous on $[a,b]$ and $M=\max \; |f(x)|$, is $M=\lim \limits_{n\to\infty} \left(\int_a^b|f(x)|^n\,\mathrm dx\right)^{1/n}$?
148782
How to prove these two limits $\lim_{n\to\infty}\frac{a_{n}}{n}$ and $\lim_{n\to\infty}\frac{a_{n+1}-a_{n}}{n}$ exist?
70790
Evaluation of $\lim_{q \to 0} (\int_0^1 |f|^q)^{1/q} $ for $f \in L^1([0,1])$.
89251
Limit $\lim\limits_{x\to0}{\frac{\ln{(e+x)}-e^x}{\cos^2{x} -e^x}}$
50673
Limit of ${a_n}^{1/n}$ is equal to $\lim_{n\to\infty} a_{n+1}/a_n$
11385
Using the Limit definition to find the derivative of $e^x$
43852
Evaluate $\lim_{x\to 0}\frac{e^{(x+1)^{1/x}}-(x+1)^{e/x}}{x^2}$
121217
How to show that $\lim\limits_{x \to \infty} f'(x) = 0$ implies $\lim\limits_{x \to \infty} \frac{f(x)}{x} = 0$?
140884
Limits and derivatives - two questions
129011
Is there limit $ \lim_{(x,y) \to (0,0)} \frac{x^3}{x^2 + y^2}$?