How to prove geometrically the limit $\lim_{x \to 0}\frac{1-\cos{x}}{x}$ using squeeze theorem
15583
Finding the limit of $(1-\cos(x))/x$ as $x\to 0$ with squeeze theorem
80542
limit of a geometric mean
148898
Limit $(0÷0)$ and use L'hopital Rule
77669
Limits of trig functions
67853
Prove existence of $\lim_{(x,y) \rightarrow (0,2)} \frac{x (y-2)^3}{3x - 5(y-2)^4}$
79785
Determining the limit $\lim_{h\to0} \frac{\cos(x+h) - \cos(x)}{(x+h)^{1/2} - x^{1/2}}$
104391
Find $\lim_\limits{x\to 1^-}{\ln x\cdot \ln(1-x)}$.
156448
Evaluate the limit without using the L'Hôpital's rule
119106
Compute: $\lim_{x\to 0}\frac{\sqrt[m]{\cos(\alpha x)}-\sqrt[n]{\cos{(\beta x)}}}{x^2},\;m,n\in\mathbb N,\alpha,\beta\in\mathbb R$
129042
Prove that $\lim_{a \to 0^{+}} \int_{0}^{a} \frac{1}{\sqrt{\cos(x)-\cos(a)}} \;dx=\frac{\pi}{\sqrt{2}}$
95962
proving a theorem from limit using Hopital rule
155979
$\lim_{x\to 0} \frac{\sin x - x}{x^2}$ without L'Hospital or Taylor
106527
Limit of $(\cos1/n)^{n^2}$ when $n\to\infty$
109899
Find $\,\lim_{x\to 1}\frac{\sqrt[n]{x}-1}{\sqrt[m]{x}-1}$
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} $?
4289
$\lim_{x\to0}\dfrac{1}{x}-\lim_{x\to0}\dfrac{1}{x}$
32743
How to prove that $\lim_{h\to 0} \, \frac{e^h-1}{h}$