Rigor in showing limit of $\frac{\cos(\Delta x)-1}{\Delta x}=0$
15583
Finding the limit of $(1-\cos(x))/x$ as $x\to 0$ with squeeze theorem
125088
show that $ \lim(\sin(\frac{1}{x}))$ as $x$ approaches zero does not exist.
45728
Proving a limit of a trigonometric function: $\lim_{x \to 2/\pi}\lfloor \sin \frac{1}{x} \rfloor=0$
6619
Prove that $\lim \limits_{(x,y,z) \to (0,0,0)} \frac{{xyz}}{{x+y+z}}=0$
155539
Evaluating the limit $\lim_{x \to 0+}\left(\frac{1}{x}-\frac{1}{\arctan(x)}\right)$
156011
Evaluate $\lim_{y\to 0} \dfrac {(x+y)\sec (x+y) - x\sec x}{y}$
128882
Prove $\lim\limits_{n\to\infty}\frac{1}{\sqrt[n]{n!}}=0$
143227
Show that: $\lim \limits_{n\to\infty}\frac{x_n-x_{n-1}}{n}=0 $
5947
Limit of a trigonometric rational expression
89251
Limit $\lim\limits_{x\to0}{\frac{\ln{(e+x)}-e^x}{\cos^2{x} -e^x}}$
123476
Prove $[\sin x]' = \cos x$ without using $\lim\limits_{x\to 0}\frac{\sin x}{x} = 1$
143375
Showing that $\lim_{(x,y) \to (0, 0)}\frac{xy^2}{x^2+y^2} = 0$
9746
Determine the following limit as x approaches 0: $\frac{\ln(1+x)}x$
158447
Limit as $(x,y)$ approaches $(0,0)$ of $(1+x^2+y^2)^{\frac{1}{x^2+y^2+xy^2}}$
73812
Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
17029
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
64860
Evaluation of $\lim\limits_{x\rightarrow0} \frac{\tan(x)-x}{x^3}$