Prove with the mean value theorem that $x-\frac{x^2}{2} < \ln(1+x)$
104688
How can I prove that $x-{x^2\over2}<\ln(1+x)$
132431
Proving $|f'(z)|\leq\frac{\text{Re}(f(z))}{\text{Re}(z)}$
140516
How does one prove the Taylor's Theorem by the Cauchy's Mean Value Theorem?
101289
Studying the equation $\ln(x)- 1+ x^2=0$
91000
Prove that $\frac{1}{a+1}0$
24469
Prove $ 2<(1+\frac{1}{n})^{n}$
122971
how to prove that $\ln(1+x)< x$
13902
Show that $\frac{1}{x_1^2}+\frac{1}{4\cdot x_2^2}+\ldots+\frac{1}{n^2\cdot x_n^2}\leq\frac{3n-2}{2n-1}$.
62443
Prove that $\sum_{n=1}^\infty \ln\left(\frac{n(n+2)}{(n+1)^2}\right)$ converges and find its sum
45742
Prove that ${\left(\frac{x+1}{2}\right)}^{x+1} \leq x^x$
45342
Generalization of Mean Value Theorem to functions, $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$
51653
Prove that $m+\frac{4}{m^2}\geq3$ for every $m > 0$
139674
Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$
145423
prove that if $1 \le m \le n$ then $\left(1+\frac1n\right)^m < 1+\frac mn + \left(\frac mn\right)^2$
30629
mean value theorem question
73240
How do I prove this form of mean value theorem for integral?
30510
Second mean value theorem proof