Prove $ \frac{1}{x+1} \le \ln(1+\frac{1}{x}) \le \frac{1}{x}$ with usage of the definition of a logarithmic function
54513
Prove $\frac 1{x+1}<\ln\left(\frac{x+1}x\right)<0.5\left(\frac 1x+\frac 1{x+1}\right)$
49408
Proof of the derivative of ln(x)
66902
Prove that $\int_{-\infty}^{\infty} \frac{e^{2x}-e^x}{x (1+e^{2x})(1+e^{x})}\mathrm{d}x=\log 2$
3110
Prove $\frac{1}{\sqrt{x}}\geq \frac{\ln x}{x-1}$
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
87055
How to prove $\frac{x}{1+x^2}0$?
91306
Integration of $\frac{1}{\log(x)}$
30385
Proving that $\frac{e^x + e^{-x}}2 \le e^{x^2/2}$
52427
Prove, $\sqrt{n} \le (n!)^\frac{1}{n} \le \frac{n+1}{2} $
124654
Prove this inequality: $\frac n2 \le \frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac1{2^n - 1} \le n$
113593
How can I prove that $\frac{n^2}{x_1+x_2+\dots+x_n} \le \frac{1}{x_1}+ \frac{1}{x_2} +\dots+ \frac{1}{x_n}$?
122115
Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
39747
Showing that $\lim_{x\to 0} x\log{x}= 0$ without using L'Hopital's rule
14952
Prove: $\frac{x}{\sqrt{y}}+\frac{y}{\sqrt{x}}\geq \sqrt{x}+\sqrt{y}$
39073
Proving that: $\forall n \in \mathbb{N} :|f^{(n)}(x)|\leq \frac{1}{n+1}$
144633
Verification of proof involving logarithms and limits
127397
$z\overline{w}\ne 1 $ Prove that $|\frac{w-z}{1-\overline{w}z}|\le 1|$ if $|z|\le 1$ and $|w|\le 1 $