Prove that $\lim_{x \to y} \frac{x^k-y^k}{x-y} = k*y^{k-1}$ for $y\in\mathbb R$ and $k\in\mathbb N$
90496
Proving $\lim \frac{x^n-a^n}{x-a}=n\cdot a^{n-1}$
95962
proving a theorem from limit using Hopital rule
17779
Proving the Limit of a Sequence of without the Dominated Convergence Theorem
22347
Proving that: $\lim\limits_{n\to\infty} \left(\frac{a^{\frac{1}{n}}+b^{\frac{1}{n}}}{2}\right)^n =\sqrt{ab}$
126256
Prove limit of function
133228
Prove $(|x| + |y|)^p \le |x|^p + |y|^p$ for $x,y \in \mathbb R$ and $p \in (0,1]$.
152440
Slick proofs that if $\sum\limits_{k=1}^\infty \frac{a_k}{k}$ converges then $\lim\limits_{n\to\infty} \frac{1}{n}\sum\limits_{k=1}^n a_k=0$
86348
Proving $\sum\limits_{k=0}^{n-1} \Bigl[x + \frac{k}{n}\Bigr] = [nx]$
13696
Proving $\limsup\frac 1 {a_n}=\frac 1 {\liminf a_n}$ and $\limsup a_n\cdot \limsup \frac 1 {a_n} \ge 1$
71798
$\lim_{n\to \infty}\frac{1}{n} \sum_{k=1}^n x_k =x\;$ given $\;\lim_{n\to \infty} x_n= x\;?$
30181
Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
44551
What is the result of $ \lim_{n \to \infty} \frac{ \sum^n_{i=1} i^k}{n^{k+1}},\ k \in \mathbb{R} $ and why?
2449
Prove that $\lim \limits_{n \to \infty} \frac{x^n}{n!} = 0$, $x \in \Bbb R$.
12083
How to prove $\limsup (x_{n}+y_{n})=\lim x_{n}+\limsup y_{n}$?
128882
Prove $\lim\limits_{n\to\infty}\frac{1}{\sqrt[n]{n!}}=0$
29287
Prove that: $\lim_{n\to\infty} f(n+1) - f(n) = \lim_{x\to\infty} (f(x))' $
110126
Prove that $\lim\limits_{(x,y) \to (0,0)} \frac{{x{y^2}}}{{{x^2} + {y^4}}} = 0$