Question Number 160949 by Ahmed777hamouda last updated on 09/Dec/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 160948 by Rustambek last updated on 09/Dec/21 $$\frac{\mathrm{1}}{\mathrm{1}\centerdot\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}\centerdot\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}\centerdot\mathrm{6}}+…+\frac{\mathrm{1}}{\mathrm{39}\centerdot\mathrm{40}}=? \\ $$ Answered by puissant last updated on 09/Dec/21 $$\Omega=\underset{{k}=\mathrm{1}} {\overset{\mathrm{39}} {\sum}}\frac{\mathrm{1}}{{k}\left({k}+\mathrm{1}\right)}\:=\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{39}} {\sum}}\left\{\frac{\mathrm{1}}{{k}}−\frac{\mathrm{1}}{{k}+\mathrm{1}}\right\} \\…
Question Number 160939 by mathlove last updated on 09/Dec/21 $${log}\underset{{ab}} {{x}}=?\:\:\:\:\:\:{if}\:\:{log}\underset{{a}} {{x}}=\mathrm{30}\:\:{andlog}\underset{{b}} {{x}}=\mathrm{70} \\ $$ Commented by blackmamba last updated on 09/Dec/21 $$\:\begin{cases}{{a}={x}^{\frac{\mathrm{1}}{\mathrm{30}}} }\\{{b}={x}^{\frac{\mathrm{1}}{\mathrm{70}}} }\end{cases}\:\Rightarrow\:\mathrm{log}\:_{{ab}}…
Question Number 160909 by naka3546 last updated on 09/Dec/21 $${How}\:\:{many}\:\:\mathrm{3}−{digits}\:\:{number}\:\:{such}\:\:{that}\:\:{sum}\:\:{of}\:\:{its}\:\:{digits}\:\:{is}\:\:\mathrm{11}\:? \\ $$ Answered by mr W last updated on 09/Dec/21 $$\boldsymbol{{METHOD}}\:\mathrm{1} \\ $$$$\left({x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +…{x}^{\mathrm{9}}…
Question Number 160908 by naka3546 last updated on 10/Dec/21 $${x},{y},{z}\:\:\in\:\:\mathbb{R}^{+} \\ $$$${Find}\:\:{the}\:\:{minimum}\:\:{value}\:\:{of}\:\:{this}\:\:{expression}\: \\ $$$$\:\:\:\:\:\:\frac{{xyz}}{\left(\mathrm{1}+\mathrm{3}{x}\right)\left({x}+\mathrm{8}{y}\right)\left({y}+\mathrm{9}{z}\right)\left(\mathrm{6}+{z}\right)}\:\: \\ $$$$ \\ $$ Commented by mr W last updated on…
Question Number 95339 by mathocean1 last updated on 24/May/20 $$\mathrm{f}\left(\mathrm{x}\right)=\mid\mathrm{2x}+\mathrm{3}\mid \\ $$$$\mathrm{f}\:'\left(\mathrm{x}\right)=…? \\ $$ Answered by john santu last updated on 24/May/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\left(\mathrm{2x}+\mathrm{3}\right)^{\mathrm{2}} } \\…
Question Number 160873 by SANOGO last updated on 08/Dec/21 Answered by TheSupreme last updated on 08/Dec/21 $$\left.\mathrm{1}\right)\:\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{1}}{{a}^{\mathrm{2}} }\frac{{dx}}{\mathrm{1}+\left(\frac{{x}}{{a}}\right)^{\mathrm{2}} }=\frac{\mathrm{1}}{{a}}{arctan}\frac{{x}}{{a}}=\frac{\pi}{\mathrm{2}{a}} \\ $$ Commented by…
Question Number 160865 by vvvv last updated on 08/Dec/21 $$\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{3}} {\boldsymbol{\mathrm{lim}}}\frac{\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)−\boldsymbol{{tan}}\left(\mathrm{3}\right)}{\boldsymbol{{sin}}\left(\boldsymbol{{ln}}\left(\boldsymbol{{x}}−\mathrm{2}\right)\right)} \\ $$$$\boldsymbol{{work}}\:\boldsymbol{{with}}\:{the}\:{rule}\:{of} \\ $$$${substitution}\:\:{of}\:{infinitely} \\ $$$${small}\:\:{functions}\:{equivalent}\: \\ $$$${to}\:{a}\:{limit} \\ $$ Commented by cortano last…
Question Number 160866 by vvvv last updated on 08/Dec/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 160848 by naka3546 last updated on 07/Dec/21 $${Find}\:\:{the}\:\:{value}\:\:{of}\:\:{a}\:\:{such}\:\:{that} \\ $$$$\:\:\:\:\:−\mathrm{2}\:<\:\frac{\mathrm{2}{x}+{a}}{{x}^{\mathrm{2}} +\mathrm{1}}\:<\:\mathrm{2} \\ $$ Answered by kowalsky78 last updated on 08/Dec/21 $${I}\:{think}\:{the}\:{correct}\:{answer}\:{is}\:{a}=−\frac{\mathrm{3}}{\mathrm{2}}. \\ $$…