Proving $x^{1/x}$ approaches $1$ as $x$ approaches infinity
30160
How to show that $\lim_{n \to +\infty} n^{\frac{1}{n}} = 1$?
60321
Use the definition of derivative to prove $\lim_{x\to 0}\ln(x+1)/x =1$
154080
circular reasoning in proving $\frac{\sin x}x\to1,x\to0$
105952
If each $a_n >0$ and $\sum a_n$ diverges, prove that $\sum a_n x^n \to +\infty$ as $x\to1^-$.
88328
Proof of $1+x\leq e^x$ for all x?
106868
Prove that $x+\frac1{4x} ≥ 1$ for $x>0$
47606
Proving $\lim_{n\to\infty} a^{\frac{1}{n}}=1$ by definition of limit
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
25772
Limit of ${x^{x^x}}$ as $x\to 0^+$
82775
if $a>1$, Prove that $\lim a^{1\over n}=1$
55266
Prove that $(n+1)^{n-1}<n^n$
141260
Prove using the formal definition of a limit that
104688
How can I prove that $x-{x^2\over2}<\ln(1+x)$
16739
The Limit of $x\left(\sqrt[x]{a}-1\right)$ as $x\to\infty$.
13533
Proof that the limit of $\frac{1}{x}$ as $x$ approaches $0$ does not exist
36906
Prove that $x^n+x^{-n} \in \mathbf{N}$ if $x+\frac1x \in \mathbf{N}$