New posts in Calculus

inequality $\left(\frac{5}{4} \right)^{\sqrt{2}}< \left(\frac{6}{5} \right)^{\sqrt{3}}$

How do I prove $\exp(1)=e$ if $\exp$ is defined in a series expansion?

Prove $\ln(a \cdot b)=\ln(a)+\ln(b)$, $a,b>0 $ and $\lim_{a \to 0} \frac{\ln(1+a)}{a} =1$.But we shall not even know that the exponential function.

Why does this Infinite Series have contradictory convergences?

Impossible integral?

How to prove this lower bound on $\log(1+x)$ for $x \geq 0$? How about $x > -1$?

Find the sum: $\sum_{n=0}^\infty \frac{(n!)^2}{(2n)!}x^n$

Computing the integral $\displaystyle I=\int_{0}^{1}\sqrt{1-x^{\pi}}dx$

How to proceed $\int \frac{dx}{(x-2) \left(1+\sqrt{7 x-10-x^2}\right)} $

Show that $f$ is bijective.