Category: Differentiation

Question Number 140055 by mnjuly1970 last updated on 03/May/21 $$$$$$provethat:$$$$\mathrm{\Omega }:={\int }_0^{\mathrm{\infty }}\frac{1-e^{-x}}{1+e^{2x}}.\frac{dx}{x}=ln\left(\frac{{\mathrm{\Gamma }}^2\left(\frac{1}{4}\right)}{4\sqrt{2\pi }}\right)$$$$\:\Theta:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\mathrm{2}{n}+\mathrm{1}}{\mathrm{2}{n}}\right)^{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} } \overset{??}…

Question Number 139949 by mnjuly1970 last updated on 02/May/21 $$$$$$\dots \dots \dots nice\dots .\ast \dots .\ast \dots .\ast \dots .calculus\left(I\right)$$$$\mathit{\varphi }={lim}_{x\to 0^{+}}{\left(\sqrt[3]{cos(\sqrt{x}}\right)}^{cot\left(x\right)}=??$$$$solution\dots \dots \dots$$$$sin\left(x\right)\approx x(x\to 0)$$$$\:\:\:\:\:\:\:\boldsymbol{\phi}:=\:\:{lim}_{{x}\rightarrow\mathrm{0}^{+} } \left\{\left({cos}\left(\sqrt{{x}}\:\right)\right)^{\frac{\mathrm{1}}{\mathrm{3}}}…

Question Number 139851 by mnjuly1970 last updated on 01/May/21 $$$$$$prove\dots \dots$$$$\mathrm{\Phi }={\int }_0^1\frac{ln\left(\frac{1}{1-x}\right)}{\sqrt{x}}dx=4ln\left(\frac{e}{2}\right)\dots ✓$$ Answered by mindispower last updated on 01/May/21…

Question Number 139694 by mnjuly1970 last updated on 30/Apr/21 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 139555 by snipers237 last updated on 28/Apr/21 $$\underset{i=0}{\prod ^5}(1-cotan(20+i))\stackrel{?}{=}8$$ Answered by mr W last updated on 28/Apr/21 $$\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{tan}\:\mathrm{20}°}\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{tan}\:\mathrm{25}°}\right) \…