How to evaluate $\lim_{x\to0} \frac{1-\cos(x)}{x^2}$ in terms of $\alpha = \lim_{x\to0} \frac{\sin(x)}{x}$?
36063
Finding the limit of $(1-\cos x)/x^2$
156231
Computing $\lim\limits_{n\to\infty} \int_{0}^{\infty}\frac{\sin(x/n)}{(1+x/n)^{n}}\, dx$
65239
Find $\lim_{x \to 0} \frac{x - \tan(x)}{x - \sin(x)}$
111636
Finding $\lim_{n\to\infty}\int_0^{\frac{1}{2^n}}(1+\cos(x))^n\,dx$
103218
Find $\lim_{(x,y) \to (0,0)} \frac{\tan(x^3+y^3)}{\sin(x^2+y^2)}$
138583
What is the limit of $\lim\limits_{x→∞}\frac{\sin x}{x}$
5947
Limit of a trigonometric rational expression
86169
How do I solve this limit: $\lim _{x \to 0} \left(\frac{ \sin x}{x}\right)^{1/x}$?
51622
Evaluating $\lim\limits_{x\rightarrow0}\frac{e^{-1/x^2}}{x}$
114675
Evaluating $\lim\limits_{x\to 0}(1+x)^{1/x}$?
27002
Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$
122145
Evaluating Limit - $(1-(\cos x)^{\sin x})/(x^3)$
79299
Strange behavior of $\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}$
150734
Solving $\lim\limits_{x\to0} \frac{x - \sin(x)}{x^2}$ without L'Hospital's Rule.
139386
Limits of trigonometric functions: $\lim _{x\to \pi } \frac{\cos(x/2)}{\pi ^2-x^2}$
86634
How to find $ \lim_{(x,y)\to(0,0)} \frac{\sin^2 (x-y)}{|x|+|y|} $?
20956
Correct way to prove the limit: $\mathop {\lim }\limits_{x \to 0} {x^\alpha }\int\limits_x^1 {\frac{{f\left( t \right)}}{{{t^{\alpha  + 1}}}}dt} $?