Is L'Hopital for $\lim\limits_{x\to0}\frac{\sin(x)}{x}$ circular?
123476
Prove $[\sin x]' = \cos x$ without using $\lim\limits_{x\to 0}\frac{\sin x}{x} = 1$
113781
How can I calculate $\lim_{x\to 0} \frac{\arctan(x)-\arcsin(x)}{x^3}$ without L'Hôpital?
122301
Evaluating and proving $\lim\limits_{x\to\infty}\frac{\sin x}x$
142404
Evaluating limit making it $\frac{\infty}{\infty}$ and using L'Hopital Rule
68136
$\lim\limits_{x\to 0} \frac{\tan x - \sin x}{x^3}$?
31146
Does the limit $\lim_{(x,y)\to (0,0)} \frac {x^3y^2}{x^4+y^6}$ exist
44336
Is $\lim\limits_{x\to x_0}f'(x)=f'(x_0)$?
123490
L'Hopital's rule and $\frac{\sin x}x$
98306
Limit of $n/\ln(n)$ without L'Hôpital's rule
106742
Evaluating $ \lim_{x \rightarrow 0}\left (\frac{\sin(x)}{x}\right)^\frac{1}{x^2}$
94168
evaluate the limit as $x$ approaches $0$ of $(\cos x-1)/x$ without l'Hopital's rule
65213
How to find $\lim\limits_{x\to0}\frac{e^x-1-x}{x^2}$ without using l'Hopital's rule nor any series expansion?
33372
What is $\lim_{x\to\infty}\left(\sin{\frac 1x}+\cos{\frac 1x}\right)^x$?
22686
Show $\lim_{h\to 0} \frac{(a^h-1)}{h}$ exists without l'Hôpital or even referencing $e$ or natural log
59890
Fundamental Theorem of Calculus for $\lim\limits_{x\to 0}\frac{\int_0^x(x-t)\sin t^2\ dt}{x\sin^3x}$
41659
Limit as $x\to 0$ of $x\sin(1/x)$
37755
Limit $\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}$