How do I evaluate this trigonometric limit: $\lim_{x\to\frac\pi4}\frac{\sqrt2\cos(x)-1}{\cot(x)-1}$?
109171
How to evaluate this trigonometric limit?
79785
Determining the limit $\lim_{h\to0} \frac{\cos(x+h) - \cos(x)}{(x+h)^{1/2} - x^{1/2}}$
76560
How do I calculate this limit: $\lim\limits_{n\to\infty}1+\sqrt[2]{2+\sqrt[3]{3+\dotsb+\sqrt[n]n}}$?
26408
Evaluate a limit (probably involving L'Hôpital rule)
35260
Evaluate the limit $\displaystyle\lim_{x \to 0}\frac{(e-\left(1 + x\right)^{1/x})}{\tan x}$.
142114
Limit as $x\to 2$ of $\frac{\cos(\frac \pi x)}{x-2} $
30259
Evaluating the double limit $\lim_{m \to \infty} \lim_{n \to \infty} \cos^{2m}(n! \pi x)$
133882
$\lim_{n\to \infty }\cos (\pi\sqrt{n^{2}-n})$ - second battle
45728
Proving a limit of a trigonometric function: $\lim_{x \to 2/\pi}\lfloor \sin \frac{1}{x} \rfloor=0$
11516
Evaluate the limit: $\lim_{(x,y,z)\to(0,0,0)}\frac{xy+yz^2+xz^2}{x^2+y^2+z^4}$
38271
Which is the easiest way to evaluate $\int \limits_{0}^{\pi/2} (\sqrt{\tan x} +\sqrt{\cot x})$?
129913
Evaluate: $I=\int\limits_{0}^{\frac{\pi}{2}}\ln\frac{(1+\sin x)^{1+\cos x}}{1+\cos x}dx$
94168
evaluate the limit as $x$ approaches $0$ of $(\cos x-1)/x$ without l'Hopital's rule
135565
Limit of $\frac{1}{x^2}-\frac{1}{\sin^2(x)}$ as $x$ approaches $0$
69309
How do I simplify and evaluate the limit of $(\sqrt x - 1)/(\sqrt[3] x - 1)$ as $x\to 1$?
7819
Calculate: $ \lim_{x \to 0 } = x \cdot \sin(\frac{1}{x}) $
150981
Why doesn't using the approximation $\sin x\approx x$ near $0$ work for computing this limit?