Let $f : R → R$ be a differentiable function and $f(x) = 0$ for $|x| ≥ 10$. Let $g(x) = \sum_{k∈Z} f(x + k)$.
117770
Let $\displaystyle f$ be differentiable, $\displaystyle f(x)=0$ for $|x| \geq 10 $ and $g(x)=\sum_{k \in \mathbb Z}f(x+k).$
20273
Prove that if $|f(x)| \leq x^2$, then the function is continuous and differentiable at $x=0$.
47026
if $f^{(n)}(x_0),g^{(n)}(x_0)$ exist and $\lim_{x\to x_0} \dfrac{f(x)-g(x)}{(x-x_0)^n}=0$ then $f^{(r)}(x_0)=g^{(r)}(x_0 )$ for all $0\leq r\leq n.$
13202
Prove that there exists at least one $x_0\in\mathbb{R}$, such that $f(x_0)+f''(x_0)=0$
34136
$f$ is differentiable in $[0,1]$ ,$\sup_{x\in[0,1]}|f'(x)| \le M\lt+\infty $
111470
Proof of differentiability of $f(x)$
17646
If $\frac{f(x)}{x}$ is decreasing in $(0,\infty)$, prove that $f(a+b) \leq f(a) + f(b)$ for $a,b >0$
137527
if $f(x)$ is differentiable at a x, prove that: $\lim_{h\to0}\frac{f(x+h)-f(x-h)}{2h}$
130322
Show that $f(x) = 0$ if $x = 0$ $f(x) = \text{exp}(-1/x^{2})$ if $x \neq 0$ is infinitely differentiable but not analytic at $x_{0} = 0$ `
26424
If $f(x)<g(x)$ prove that $\lim f(x)<\lim g(x)$
143491
Show that $f$ is differentiable on $(−1, 1)$.
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
145265
A non-zero function satisfying $g(x+y) = g(x)g(y)$ must be positive everywhere
121771
Proof $f(x)\equiv 0$
133505
Let $f(n)=\sum_{k=0}^{\left\lfloor n/2\right\rfloor} {2k \choose k}{n \choose 2k}$ . Show that $\sum_{n\geq 0}^{} f(n)x^n=\frac{1}{\sqrt{1-2x-3x^2}}$
85480
Let $f(x,y)=\frac{x^3-y^3}{x^2+y^2}$. Is f differentiable in $(0,0)$?
16375
Is the function differentiable at $0$?