f is differentiable, $f'$ is continuous, $f_n(x) = \frac{f(x+\frac{1}{n}) - f(x)}{\frac{1}{n}}$. Show that $f_n \rightrightarrows f'$
88147
Show that $g_n(x)=nf(x+1/n)-nf(x)$ converges uniformly to $f'$
77267
Given $f$ is continuous and $f(x)=f(e^{t}x)$ for all $x\in\mathbb{R}$ and $t\ge0$, show that $f$ is constant function
80643
Show that f(x) defined on [0,infinity) R to is continuous at 0.
97256
For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
147203
How to show that $\lim_{n\to\infty}\left\{f(c+\frac{1}{n^2})+f(c+\frac{2}{n^2})+\cdots+f(c+\frac{n}{n^2})-nf(c)\right\}=\frac{1}{2} f'(c)$
112923
Let $f:\mathbb{R}\longrightarrow \mathbb{R}$ a differentiable function such that $f'(x)=0$ for all $x\in\mathbb{Q}$
105084
Let f be a function twice differentiable and with derivatives continuous on an interval $[a,b]$ containing $0$. Prove the following statement:
108060
Suppose $f:[0,\infty]\rightarrow$ to R and has continuous $f'(x)$ and $f''(x)$ f(x) → 0 as x → ∞. Show that f′(x)→0 as x→∞
131357
Prove that $f(x,y)=xy$ is differentiable using the definition
23294
Show that the function $f = \frac{xy}{x^2 + y^2}$ is continuous along every horizontal and every vertical line
144013
If $f$ is differentiable at $x = x_0$ then $f$ is continuous at $x = x_0$.
58943
If $f'(x)\le g'(x)$, prove $f(x)\le g(x)$
49408
Proof of the derivative of ln(x)
94944
Differentiable functions satisfying $f'(f(x))=f(f'(x))$
21879
Show that if $\lim_{x\to a}f'(x) = A$ then $f'(a)$ exists and equals A
129856
Show that $f(x)=\frac{x}{1+|x|}$ is uniformly continuous.
82405
For f continuous on $[0,1]$, show that there exist points $\alpha_k$ such that $\sum \limits_{k=1}^n \frac{1}{f'(\alpha_k)} = n $