Showing $\frac{x}{1+x}0$ using the mean value theorem
43226
Intuition behind logarithm inequality: $1 - \frac1x \leq \log x \leq x-1$
132738
Showing $\lim_{n \to \infty} m(E_n) = 0$, assuming $f > 0$ a.e. and $\lim_{n \to \infty} \int_{E_n}f \,dm =0$
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
60831
Need hint for $\lim_{x\to 0} \frac{(x+1)^\frac{1}{x}-e}{x}$
30510
Second mean value theorem proof
62524
Showing that $\int\limits_{-a}^a \frac{f(x)}{1+e^{x}} \mathrm dx = \int\limits_0^a f(x) \mathrm dx$, when $f$ is even
149102
Evaluating $\lim_{x \to 0} x\sin\left(\frac{1}{x}\right)$ or showing it does not exist
73240
How do I prove this form of mean value theorem for integral?
11129
Show that $\int_0^ \infty \frac{1}{1+x^n} dx= \frac{ \pi /n}{\sin(\pi /n)}$ , where $n$ is a positive integer.
157432
How to use the Mean Value Theorem to prove the following statement:
13533
Proof that the limit of $\frac{1}{x}$ as $x$ approaches $0$ does not exist
88782
Finding the limit of $x_1=0 , x_{n+1}=\frac{1}{1+x_n}$
78319
Show that $x \mapsto \frac{f(x)}{x}$ is strictly increasing on (0,1) given that f '(x) is strictly increasing on (0,1) and that f(0)=0
143375
Showing that $\lim_{(x,y) \to (0, 0)}\frac{xy^2}{x^2+y^2} = 0$
139420
How do I use the Intermediate Value Theorem in this question?
11387
Mean Value Theorem: $\frac{2}{\pi}<\frac{\sin x}{x}<1$
82612
Show that $\frac c {1+c} \le \frac a {1+a} + \frac b {1+b}$ , for $c \le a+b$ and $a,b,c \ge 0$