Prove $\frac{\ln x}{x-1} \leq \frac{1}{\sqrt{x}}$ using derivatives
3110
Prove $\frac{1}{\sqrt{x}}\geq \frac{\ln x}{x-1}$
99753
How to prove $\int_0^1\frac{1-x}{(\ln x)(1+x)}\ dx=\ln\left(\frac2{\pi}\right)$?
104807
Prove the inequality $\left|\frac{m}{n}-\frac{1+\sqrt{5}}{2}\right|<\frac{1}{mn}$
122971
how to prove that $\ln(1+x)< x$
53767
How to prove that derivatives have the Intermediate Value Property
97558
Prove that $\left| f'(x)\right| \leq \sqrt{2AC}$ using integration
126959
Prove $ \frac{1}{x+1} \le \ln(1+\frac{1}{x}) \le \frac{1}{x}$ with usage of the definition of a logarithmic function
61782
How to prove that $f(x) = \frac{-2x+1}{(2x-1)^2-1}$ is one-to-one on $(0,1)$?
21802
Prove $\sum_{d \leq x} \mu(d)\left\lfloor \frac xd \right\rfloor = 1 $
1641
Proving $f' = - \frac{\partial{F}/\partial{x}}{\partial{F}/\partial{y}}$
7404
Induction and convergence of an inequality: $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\leq \frac{1}{\sqrt{2n+1}}$
93408
Trying to show that $\ln(x) = \lim_{n\to\infty} n(x^{1/n} -1)$
66082
Using $\sqrt{1-t}\leq 1-\frac t2$ to show that $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots2n}\geq\frac1{2\sqrt n}$
105047
Prove the inequality $|xy|\leq\frac{1}{2}(x^2+y^2)$
12020
Prove $\sqrt{n+1}-\sqrt{n}\lt \frac{1}{2\sqrt{n}}$
115712
Application of Derivatives rigorous proof
103757
how can I prove that $\frac{\arctan x}{x }< 1$?