Why does $\lim_{x\to0}\frac{\sin(x)}{x}$ equal $1$?
17029
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
106142
Why does L'Hopital's rule fail in calculating $\lim_{x \to \infty} \frac{x}{x+\sin(x)}$?
151329
Showing $\lim_{(x,y) \to (0,0)} \sin (xy) / xy = 1$
80060
Is $\frac{1}{\infty}$  equal zero?
104158
$\frac 00=$ ? Why It is un answerable?
135565
Limit of $\frac{1}{x^2}-\frac{1}{\sin^2(x)}$ as $x$ approaches $0$
73812
Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
149102
Evaluating $\lim_{x \to 0} x\sin\left(\frac{1}{x}\right)$ or showing it does not exist
125088
show that $ \lim(\sin(\frac{1}{x}))$ as $x$ approaches zero does not exist.
73786
Limit of $\frac{\sin(x+y)}{x+y}$ as $(x,y) \to (0,0)$
55577
Why is $\frac{1}{\infty } \approx 0 $ and $ \frac{1}{0} = {\infty}$?
102408
Evaluate the limit $\lim_{x \to 0}{\frac{\sqrt{1+x\sin{x}}-\sqrt{\cos{2x}}}{\tan^{2}{\frac{x}{2}}}}$
7819
Calculate: $ \lim_{x \to 0 } = x \cdot \sin(\frac{1}{x}) $
45728
Proving a limit of a trigonometric function: $\lim_{x \to 2/\pi}\lfloor \sin \frac{1}{x} \rfloor=0$
53109
Why is this limit $\lim_{n \to \infty}(1 + \frac{1}{n})^n$ equal to $e$?
70742
Evaluate $\lim_{x\rightarrow 0} \frac{\sin (6x)}{\sin(2x)}$ without L'Hopital
85249
Evaluating: $\lim\limits_{x\to0}\left(\frac{\sin x}{x}\right)^{{6}/{x^{2}}}$