Counterexample for $\lim \limits_{x \to c} \left\lvert f(x) \right\rvert = \left\lvert L \right\rvert$ then $\lim \limits_{x \to c} f(x) = L$
102540
Limits, find a limit that exist in absolute value but not outside the absolute value.
130161
Showing that if $\lim_{x\to\infty}xf(x)=l,$ then $\lim_{x\to\infty}f(x)=0.$
151568
Limit Integral equal to a supremun: $\lim_{n\to \infty} \left[\int_a^b (f(x))^n dx\right]^{{1}/{n}}=\sup_{x\in [a,b]} f(x).$
72960
How to prove this limit composition theorem?
45988
limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$
31872
Two similar limit problems
149586
If $\lim_{x\to\infty} f'(x) = L$, prove that $\lim_{x\to\infty} f(x+c)-f(x) = cL$ and $\lim_{x\to\infty} f(x)/x=L$
77623
Limit of ratio ${f(x)\over x}$ equal to limit of difference $f(x+1)-f(x)$.
128761
An $\varepsilon-\delta$ proof of $\lim_{x\rightarrow c} (2x^ 2 − 3x + 4) = 2c ^2 − 3c + 4$.
68700
Proving Two Limits Are Equal to Each Other
49497
$\lim a_n = 0$ if $\left|\frac{a_{n +1}}{a_n}\right|\to L < 1$
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?
85412
Epsilon delta proof for $\lim_\limits{x\to a} \sqrt{x} = \sqrt{a}$ where $a>0$
73812
Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
150995
Show that $\liminf(\sqrt{x_n})=\sqrt{\liminf x_n}$
3979
Limit comparison test proof
121085
Showing that $\lim\limits_{x \rightarrow 0} \frac{1}{x}$ does not exist.