Prove $\lim_{x\rightarrow c} \sin x =\sin c$ using $\epsilon$-$\delta$ definition
17029
How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
59839
In $\epsilon$-$\delta$ continuity over an interval, $|x-c|<\delta$ implies $|f(x)-f(c)|<\epsilon$. Since both $c$ and $x$ vary, what's the difference?
1371
Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
126736
Show that $\lim_{\epsilon\to0^{+}}\frac{1}{2\pi i}\int_{\gamma_\epsilon}\frac{f(z)}{z-a} \, dz=f(a)$
22575
Prove that $\lim\limits_{n\rightarrow\infty} \left(1+\frac{1}{a_{n}} \right)^{a_{n}}=e$ if $\lim\limits_{n\rightarrow\infty} a_{n}=\infty$
111205
Proving that $\lim_{k\to \infty}\frac{f(x_k)-f(y_k)}{x_k-y_k}=f'(c)$ where $\lim_{k\to \infty}x_k=\lim_{k\to \infty}y_k=c$ with $x_k<c<y_k$
145614
Proving one limit is equal to another
11879
If $\lim_{n\rightarrow\infty} f(n+1) - f(n) = L$, prove that $\lim_{n\rightarrow\infty} f(n)/n = L$
53213
How to prove that $\lim(\underset{k\rightarrow\infty}{\lim}(\cos(|n!\pi x|)^{2k}))=\chi_\mathbb{Q}$
132873
Understanding Epsilon-Delta Proof
135534
Prove that $\lim_{x\to 2}x^2=4$ using $\epsilon-\delta$ definition.
54304
How to make sense out of the $\epsilon-\delta$ definition of a limit?
78941
proof that an alternative definition of limit is equivalent to the usual one
94910
How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
145233
How to show $\lim_{n \rightarrow \infty} \int_0^1 n x^n f(x) \; dx = f(1)$ for continuous $f$?
65662
Prove $\forall K > 0: \lim_{n\rightarrow\infty} \sqrt[n]{K} = 1$
135359
How to prove that limit doesn't exist using epsilon-delta definition?