Prove that if $f(x) = \frac{\sqrt{x} - \sqrt{a}}{x-a}$, then $f$ has a limit at a.
122003
From the limit definition of differentiability, determine where the function $f(x) = \sqrt{x}$ is differentiable?
62524
Showing that $\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$, when $f$ is even
139111
Prove that $a<c<b$, $\frac{f(b)-f(a)-(b-a)f'(a)}{g(b)-g(a)-(b-a)g'(a)}=\frac{f"(c)}{g"(c)}$
17029
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
145496
Show $\lim_{h \to \ 0} \frac{f(x + 2h) - 2f(x+h) + f(x)}{h^{2}} = f''(x)$ Proof verification
95397
Finding out the limit $\lim_{a \to \infty} \frac{f(a)\ln a}{a}$
29287
Prove that: $\lim_{n\to\infty} f(n+1) - f(n) = \lim_{x\to\infty} (f(x))' $
17646
If $\frac{f(x)}{x}$ is decreasing in $(0,\infty)$, prove that $f(a+b) \leq f(a) + f(b)$ for $a,b >0$
60036
How to prove this limit exists: $a_{n+2}=\sqrt{a_{n+1}}+\sqrt{a_{n}}$
16739
The Limit of $x\left(\sqrt[x]{a}-1\right)$ as $x\to\infty$.
157577
Prove that $\lim_{x\to y} \frac{d(x, F )}{|x−y|} = 0$ for a.e. $y \in F$.
40487
Given $\lim_{x \rightarrow a}f(x)+\frac1{\left|f(x)\right|}=0$, what is $\lim_{x \rightarrow a}f(x)$?
150699
Show that if $f'$ is strictly increasing, then $\frac{f(x)}{x}$ is increasing over $(0,\infty)$
157539
Prove: $\lim\limits_{n\to\infty}\frac{1}{n}\sum\limits_{k=1}^{n}\sqrt{1+\frac{k}{n}}=\frac{2}{3}(2\sqrt{2}-1)$
119053
How to prove that $\displaystyle f''(a)=\lim_{h \to 0}\frac{f(a+2h)-2f(a+h)+f(a)}{h^2}$
4345
Prove that lim $(\sqrt{n^2+n}-n) = \frac{1}{2}$
141260
Prove using the formal definition of a limit that