Why does $\lim_{x\rightarrow 0}\frac{\sin(x)}x=1$?
17029
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
101731
What is $\lim_{(x,y)\rightarrow(0,0)} \frac{x^3-y^3}{x^2-y^2}$?
112481
Given $a_{n+1} = \frac{{a_n}}{\sin({a_n})}$ with $0 < a_1 < \frac{\pi}{2}$. Show that the limit $\lim_{n\rightarrow\infty}{a_n}$ exists and find it.
97326
Find $\lim_{x \to 0} (\frac{\tan(x)}{x})^{\frac{1}{x}}$
128218
If $\lim \limits_{x \to a}\left(f(x)+\frac{1}{f(x)}\right)=2,$ then $\lim \limits_{x \to a}f(x)=1$
145043
How do I calculate $\lim_{x\rightarrow 0} x\ln x$
33372
What is $\lim_{x\to\infty}\left(\sin{\frac 1x}+\cos{\frac 1x}\right)^x$?
125088
show that $ \lim(\sin(\frac{1}{x}))$ as $x$ approaches zero does not exist.
105064
What is wrong with this fake proof that $\lim\limits_{n\rightarrow \infty}\sqrt[n]{n!} = 1$?
80314
Finding $\lim\limits_{x\to 0}\frac{\sin{3x}}{x}$
95991
How to solve $\lim_{x \rightarrow 0} {\frac{(1+x)^a-1}{x}}$?
155539
Evaluating the limit $\lim_{x \to 0+}\left(\frac{1}{x}-\frac{1}{\arctan(x)}\right)$
60498
Prove that $\lim_{(x,y)\rightarrow(0,0)} \frac{|x|^{a}|y|^{b}}{|x|^{c} + |y|^{d}}$ does not exist
106142
Why does L'Hopital's rule fail in calculating $\lim_{x \to \infty} \frac{x}{x+\sin(x)}$?
65239
Find $\lim_{x \to 0} \frac{x - \tan(x)}{x - \sin(x)}$
150981
Why doesn't using the approximation $\sin x\approx x$ near $0$ work for computing this limit?
133405
$\lim_{x \rightarrow 0} f'(x) = L$ exists, does it follow that $f'(0)$ exists?