Show that $\lim_{x \rightarrow 0} \frac{\sin(x)}{x} = 1$ without using L'Hopital's rule
17029
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
67853
Prove existence of $\lim_{(x,y) \rightarrow (0,2)} \frac{x (y-2)^3}{3x - 5(y-2)^4}$
155979
$\lim_{x\to 0} \frac{\sin x - x}{x^2}$ without L'Hospital or Taylor
80277
How to show that $\lim \frac{1}{n} \sum_{i=1}^n \frac{1}{i}=0 $?
19056
Find the limit of $(2\sin x-\sin 2x)/(x-\sin x)$ as $x\to 0$ without L'Hôpital's rule
155188
How do I prove this limit does not exist: $\lim_{x\rightarrow 0} \frac{e^{1/x} - 1}{e^{1/x} + 1} $
151329
Showing $\lim_{(x,y) \to (0,0)} \sin (xy) / xy = 1$
53307
how to strictly prove $\sin x<x$ for $0<x<\frac{\pi}{2}$
50509
Prove that $\int_0^4 \frac{\ln x}{\sqrt{4x-x^2}}~dx=0$ (without trigonometric substitution)
113765
$\lim_{x\to0} \frac{x-\sin x}{x-\tan x}$ without using L'Hopital
86409
Show that $\lim_{x \to +\infty}\left(f(x)+f'(x)\right)=0 \Rightarrow \lim_{x \to +\infty} f(x)=0$
65239
Find $\lim_{x \to 0} \frac{x - \tan(x)}{x - \sin(x)}$
100893
Determine $\lim_{x \to 0}{\frac{x-\sin{x}}{x^3}}=\frac{1}{6}$, without L'Hospital or Taylor
13533
Proof that the limit of $\frac{1}{x}$ as $x$ approaches $0$ does not exist
98392
Value of the limit $\lim_{x \to 0} \frac{\sin(\frac{1}{x})}{\sin(\frac{1}{x})}$
13249
Multivariable limit proof: $\lim\limits_{(x,y)\rightarrow (0,0)}\frac{\left|x\right|^a\left|y\right|^b}{\left|x\right|^c + \left|y\right|^d} = 0$
6619
Prove that $\lim \limits_{(x,y,z) \to (0,0,0)} \frac{{xyz}}{{x+y+z}}=0$