How can I solve $\lim_{x \to \infty} (\cos \frac {1}{x})^{x^2}$ without differentiation/l'Hospital/Taylor Series?
106527
Limit of $(\cos1/n)^{n^2}$ when $n\to\infty$
14385
Solve $\int \limits_{0}^{\infty} \frac{\cos(x)}{\cosh(x)} dx$ without complex integration.
139386
Limits of trigonometric functions: $\lim _{x\to \pi } \frac{\cos(x/2)}{\pi ^2-x^2}$
90431
Compute $\lim_{x\to 0} \frac{e^{-1/x^2}}{x}$ without using L'Hopital?
101536
Difficult limit evaluation: $\lim_{x\to\infty}(\sqrt{x^2+4x} - x)$
79684
Finding $\lim \limits_{x \to 0} \frac{1 - \cos x}{x}$, given $\lim \limits_{x \to 0} \frac{\sin x}{x} = 1$
119106
Compute: $\lim_{x\to 0}\frac{\sqrt[m]{\cos(\alpha x)}-\sqrt[n]{\cos{(\beta x)}}}{x^2},\;m,n\in\mathbb N,\alpha,\beta\in\mathbb R$
41203
Finding $\lim\limits_{x \to \infty} (\sqrt{9x^2+x} - 3x)$
123476
Prove $[\sin x]' = \cos x$ without using $\lim\limits_{x\to 0}\frac{\sin x}{x} = 1$
92176
Solving $\lim_{n\to\infty}(n\int_0^{\pi/4}(\tan x)^ndx)$?
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?
19056
Find the limit of $(2\sin x-\sin 2x)/(x-\sin x)$ as $x\to 0$ without L'Hôpital's rule
113289
finding the limit $\lim\limits_{x \to \infty }(\frac{1}{e}(1+\frac{1}{x})^x)^x$
30259
Evaluating the double limit $\lim_{m \to \infty} \lim_{n \to \infty} \cos^{2m}(n! \pi x)$
106867
Limit of $\cos(x)/x$ as $x$ approaches $0$
18156
Find $\lim_{x\to \infty} \ln(x+1)/(\ln(x))$
133279
Does $\lim_{n\to\infty}\underset{n}{\underbrace{\cos(\cos(...\cos x))}}$ exist?