Question Number 569 by userid1 last updated on 28/Jan/15 $$\int\:\frac{\mathrm{4}{e}^{{x}} +\mathrm{6}{e}^{−{x}} }{\mathrm{9}{e}^{{x}} −\mathrm{4}{e}^{−{x}} }\:{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131642 by liberty last updated on 07/Feb/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{area}\: \\ $$$$\mathrm{of}\:\mathrm{ellipse}\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{a}^{\mathrm{2}} }+\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{b}^{\mathrm{2}} }=\mathrm{1}\:\mathrm{which}\:\mathrm{touches} \\ $$$$\mathrm{the}\:\mathrm{line}\:\mathrm{y}\:=\:\mathrm{3x}+\mathrm{2}. \\ $$ Answered by benjo_mathlover last updated…
Question Number 66105 by Rio Michael last updated on 09/Aug/19 $${Find}\:\:\int_{−\mathrm{1}} ^{\mathrm{1}} \frac{\mathrm{9}\:+\mathrm{4}{x}^{\mathrm{2}} }{\mathrm{9}−\mathrm{4}{x}^{\mathrm{2}} }\:{dx} \\ $$ Commented by Prithwish sen last updated on 09/Aug/19…
Question Number 131637 by rs4089 last updated on 07/Feb/21 Answered by Dwaipayan Shikari last updated on 07/Feb/21 $$\int_{−\infty} ^{\infty} \frac{{sinx}}{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{dx}=\int_{−\infty} ^{\infty} \frac{{sinx}}{{x}}−\frac{{xsinx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{dx}=\pi−\frac{\pi}{{e}} \\…
Question Number 66102 by Rio Michael last updated on 09/Aug/19 $${prove}\:{by}\:{mathematical}\:{induction}\:{that}\:\:\mathrm{4}^{{n}} +\mathrm{3}^{{n}} +\mathrm{2}\:{is}\:{a}\:{multiple}\:{of}\:\mathrm{3}\:{for}\:{all}\: \\ $$$${positive}\:{integral}\:{values}\:{of}\:{n}. \\ $$ Commented by mathmax by abdo last updated on…
Question Number 66103 by Rio Michael last updated on 09/Aug/19 $${A}\:{binary}\:{relation}\:{R}\:{is}\:{defined}\:{on}\:\mathbb{N},{the}\:{set}\:{of}\:{natural}\:{numbers}\:{by}\: \\ $$$$\:_{{x}} {R}_{{y}} \:\Leftrightarrow\:\exists\:{n}\:\in\:\mathbb{Z}\::\:{x}\:=\:\mathrm{2}^{{n}} {y},\:\:{x},{y}\:\in\:\mathbb{N} \\ $$$${show}\:{that}\:{R}\:{is}\:{an}\:{equivalence}\:{relation} \\ $$ Commented by Prithwish sen last…
Question Number 66101 by Rio Michael last updated on 09/Aug/19 $${find}\:\frac{{dy}}{{dx}}\:\:{when}\:{y}\:=\:{x}^{\mathrm{2}} {ln}\left(\mathrm{3}{x}\right) \\ $$$${Given}\:{that}\:{xsinx}\:−\:{y}^{\mathrm{2}} =\mathrm{0}\:{show}\:{that}\:\:{y}^{\mathrm{2}} \:=\:\mathrm{2}{cosx}\:−\mathrm{2}\left(\frac{{dy}}{{dx}}\right)^{\mathrm{2}} \:−\mathrm{2}{y}\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} } \\ $$ Commented by Prithwish sen…
Question Number 66098 by aliesam last updated on 09/Aug/19 Commented by Prithwish sen last updated on 09/Aug/19 $$\left(\mathrm{cosx}+\boldsymbol{\mathrm{i}}\mathrm{sinx}\right)^{\mathrm{5}} =\mathrm{cos5x}+\boldsymbol{\mathrm{i}}\mathrm{sin5x}\:=\:\mathrm{cos}^{\mathrm{5}} \mathrm{x}+\mathrm{5}\boldsymbol{\mathrm{i}}\mathrm{cos}^{\mathrm{4}} \mathrm{xsinx}−\mathrm{10cos}^{\mathrm{3}} \mathrm{xsin}^{\mathrm{2}} \mathrm{x}−\mathrm{10}\boldsymbol{\mathrm{i}}\mathrm{cos}^{\mathrm{2}} \mathrm{xsin}^{\mathrm{3}} \mathrm{x}+\mathrm{5cosxsin}^{\mathrm{4}}…
Question Number 66099 by olalekan2 last updated on 09/Aug/19 $${differentiate}\:{y}=\mathrm{10}^{\mathrm{1}−{sin}^{\mathrm{2}} \mathrm{3}{x}} \\ $$ Commented by mathmax by abdo last updated on 09/Aug/19 $${y}\left({x}\right)\:=\mathrm{10}^{\mathrm{1}−{sin}^{\mathrm{2}} \left(\mathrm{3}{x}\right)} \:\Rightarrow{y}\left({x}\right)\:={e}^{\left(\mathrm{1}−{sin}^{\mathrm{2}}…
Question Number 131635 by liberty last updated on 07/Feb/21 $$ \\ $$$$\mathrm{three}\:\mathrm{subject}\:\mathrm{group}\:\mathrm{are}\:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{formed}\:\mathrm{randomly}\:\mathrm{by}\:\mathrm{15}\:\mathrm{students} \\ $$$$\left(\mathrm{including}\:\mathrm{3}\:\mathrm{girls}\right)\:\mathrm{under}\:\mathrm{the} \\ $$$$\mathrm{condition}\:\mathrm{that}\:\mathrm{each}\:\mathrm{groups} \\ $$$$\mathrm{consist}\:\mathrm{5}\:\mathrm{students}\:\mathrm{and}\:\mathrm{each} \\ $$$$\mathrm{student}\:\mathrm{attends}\:\mathrm{only}\:\mathrm{one}\:\mathrm{group}. \\ $$$$\mathrm{flnd}\:\mathrm{the}\:\mathrm{probabilities}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the} \\…