Why doesn't L'hopitals Rule work for $\lim\limits_{x \to \infty} \frac{x+ \sin x}{x+ 2 \sin x}$?
134971
Why doesn't L'Hospital's rule work in this case?
116013
Problem applying L'Hopitals rule.
17069
Limit $\lim_{x\to \infty} \frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x+2}+\sqrt{x}-\sqrt{4x+12}}$
7309
Why $\lim\limits_{n\to \infty}\left(1+\frac{1}{n}\right)^n$ doesn't evaluate to 1?
51212
How do I solve $\lim\limits_{x\to\infty} \ \frac{\ln \ x}{x} = 0$?
64001
What is the result of $\lim\limits_{x \to 0}(1/x - 1/\sin x)$?
63289
Does $\sum\limits_{x=1}^\infty\sin(x)$ converge?
148170
Difficulty in evaluating a limit: $\lim_{x \to \infty} \frac{e^x}{\left(1+\frac{1}{x}\right)^{x^2}}$
81537
Limit: $\lim_{x\to 0}\frac{\tan3x}{\sin2x}$
138930
What does $\lim\limits_{x \to \infty} f(x) = 1$ say about $\lim\limits_{x \to \infty} f'(x)$?
30937
How do I find $\lim\limits_{x \to 0} x\cot(6x) $ without using L'hopitals rule?
65266
A limit problem $\lim\limits_{x \to 0}\frac{x\sin(\sin x) - \sin^{2}x}{x^{6}}$
127125
Can the limit $\lim_{h \to 0}\frac{f(x + h) - 2f(x) + f(x - h)}{h^2}$ exist if $f'(x)$ does not exist at $x$?
86169
How do I solve this limit: $\lim _{x \to 0} \left(\frac{ \sin x}{x}\right)^{1/x}$?
70086
Limit without l'Hopital or Taylor series: $\lim\limits_{x \to 0} \frac{x\cos x- \sin x}{x^3}$
91290
Evaluating $\lim_{n \to \infty} \int_{0}^{\pi} \frac{\sin x}{1+\cos ^2(nx)} dx$
39798
Computing $\lim_{n \to \infty} \int_0^{n^2} e^{-x^2}n\sin\frac{x}{n}\,dx$?