Is using L'Hospital's Rule to prove $\lim \limits_{x \to 0} \sin{x}/x$ circular?
123490
L'Hopital's rule and $\frac{\sin x}x$
39148
Does $\lim_{(x,y)\to(0,0)}[x\sin (1/y)+y\sin (1/x)]$ exist?
79299
Strange behavior of $\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}$
20764
Is it true that $\lim\limits_{x\to\infty}{x·P[X>x]}=0$?
138583
What is the limit of $\lim\limits_{x→∞}\frac{\sin x}{x}$
91278
The limit for $x\to 0$ of $x^3\sin (x)$ exists
150308
How to prove that $\lim\limits_{n\to\infty}\int\limits _{a}^{b}\sin\left(nt\right)f\left(t\right)dt=0\text { ? }$
41659
Limit as $x\to 0$ of $x\sin(1/x)$
126701
How to prove that $d \sin(x)/dx = \cos(x)$ without circular logic such as L'Hôpital's rule?
33372
What is $\lim_{x\to\infty}\left(\sin{\frac 1x}+\cos{\frac 1x}\right)^x$?
68835
Trigonometric limit: Dividing the Numerator and Denominator by $\theta\;?$
68136
$\lim\limits_{x\to 0} \frac{\tan x - \sin x}{x^3}$?
13104
What is $\lim_{x \to \infty} \frac{\sin x}{\sin x}?$
19056
Find the limit of $(2\sin x-\sin 2x)/(x-\sin x)$ as $x\to 0$ without L'Hôpital's rule
120493
L'hopitals rule with limits
113765
$\lim_{x\to0} \frac{x-\sin x}{x-\tan x}$ without using L'Hopital
98392
Value of the limit $\lim_{x \to 0} \frac{\sin(\frac{1}{x})}{\sin(\frac{1}{x})}$