Find a function $f$ such that $\lim_{x\to{}0}{f(x^2)}$ exists, but $ \lim_{x\to{}0}{f(x)}$ does not.
115132
Give an example about limits: $\lim\limits_{x\to0}f(x^{2})$ exists but $\lim\limits_{x\to0}f(x)$ does not.
52632
$f\colon(0,\infty)\to \mathbb R$ be continuous ; $f(x)\le f(nx) , \forall n \in \mathbb N , \forall x >0$ , then $\lim_{x\to \infty} f(x)$ exists?
141945
Why is $f(x) = \sqrt{x}$ is continuous at $x=0$? Does $\lim_{x \to 0^{-}} \sqrt{x}$ exist?
59279
Example of function that is differentiable, but the second derivative is not defined
119200
When does $\lim_{n\to\infty}f(x+\frac{1}{n})=f(x)$ a.e. fail
153510
Questions about the existence of a function
80720
What paths to choose to prove that $\lim_{(x,y) \to (0,0)}\frac{xy^2}{x^2 - y^2}$ does not exist?
54830
Find the limit $\lim\limits_{x\to\infty} f(x)= \lim\limits_{x \to \infty} \left(\frac{x}{x+1}\right)^x$
71225
$f(0)=0$ and $\lim_{x \to \infty}f(x)=0$. Show there's $x_0$ such that $f'(x_0)=0$
103241
A function that is continuous at the origin but not differentiable there
122762
Proving that the limit doesn't exist for $x$ other than $0$
102540
Limits, find a limit that exist in absolute value but not outside the absolute value.
109540
Simplify limit problem $\lim\limits_{x\to 0}\frac{\sqrt{2+x^2}-\sqrt{2+x^2}}{x^2}$
90284
A function that is $L^p$ for all $p$ but is not $L^\infty$?
135610
How to give an example of a $f$ differentiable in a deleted neighborhood of $x_0$ such that $\lim_{x\to x_0}f^\prime(x)$ doesn't exist?
89257
Give an example of a function $f:\mathbb{R}^2 \mapsto \mathbb{R}^2$ such that
129579
If $f''(x_0)$ exists then $\lim_{x \to x_0} \frac{f(x_0+h)-2f(x_0)+f(x_0-h)}{h^2} = f''(x_0)$