Question Number 141775 by mathmax by abdo last updated on 23/May/21 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } }{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by qaz last updated…
Question Number 141774 by mathmax by abdo last updated on 23/May/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 141769 by 7770 last updated on 23/May/21 $$\boldsymbol{\mathrm{If}}\:\:\boldsymbol{\mathrm{y}}=\mathrm{2}\boldsymbol{\mathrm{sinx}}+\boldsymbol{\mathrm{tanx}},\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }=\mathrm{2}\boldsymbol{\mathrm{sinx}}\left(\boldsymbol{\mathrm{sec}}^{\mathrm{3}} \boldsymbol{\mathrm{x}}−\mathrm{1}\right) \\ $$$$\boldsymbol{\mathrm{Any}}\:\boldsymbol{\mathrm{detailed}}\:\boldsymbol{\mathrm{solution}}\:\boldsymbol{\mathrm{please}}. \\ $$ Answered by physicstutes last updated on…
Question Number 141768 by loveineq last updated on 23/May/21 $$\mathrm{Let}\:{a},{b},{x},{y}\:>\:\mathrm{0}\:\mathrm{and}\:\left({a}+{x}\right)\left({b}+{y}\right)\:=\:\left({a}+{b}\right)^{\mathrm{2}} \:.\:\:\:\:\:\:\:\: \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}−{y}}{{x}}+\frac{{b}−{x}}{{y}}\:\leqslant\:\frac{{b}−{x}}{{a}}+\frac{{a}−{y}}{{b}}\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 76232 by Rio Michael last updated on 25/Dec/19 $${how}\:{do}\:{we}\:{find} \\ $$$$\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:{sinh}^{−\mathrm{1}} {x}\:{dx}\:{and}\:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\mathrm{cosh}\:^{−\mathrm{1}} {xdx} \\ $$ Commented by mr W…
Question Number 10696 by okhema last updated on 23/Feb/17 $${given}\:{that}\:{tan}\mathrm{2}{x}=\frac{\mathrm{1}}{\mathrm{4}}{and}\:{that}\:{angle}\:{x}\:{is}\:{acute},\:{calculate},{without}\:{using}\:{a}\:{calculator}\:{the}\:{value}\:{of}\:{these}. \\ $$$$\left({a}\right)\:{cos}\mathrm{2}{x} \\ $$$$\left({b}\right)\:{sinx} \\ $$$$ \\ $$ Answered by mrW1 last updated on 23/Feb/17…
Question Number 10695 by okhema last updated on 23/Feb/17 $${prove}\:{that}\:{tanx}−{cotx}=−\mathrm{2}{cot}\mathrm{2}{x} \\ $$ Answered by nume1114 last updated on 23/Feb/17 $$\:\:\:\:\mathrm{tan}\:{x}−\mathrm{cot}\:{x} \\ $$$$=\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}−\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}} \\ $$$$=\frac{\mathrm{sin}^{\mathrm{2}} {x}−\mathrm{cos}^{\mathrm{2}}…
Question Number 10694 by ABD last updated on 23/Feb/17 Answered by mrW1 last updated on 23/Feb/17 $${f}\left(\mathrm{3}{x}^{\mathrm{4}} +{x}^{\mathrm{3}} \right)=\mathrm{6}{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}} −\mathrm{3}=\mathrm{2}\left(\mathrm{3}{x}^{\mathrm{4}} +{x}^{\mathrm{3}} \right)−\mathrm{3} \\ $$$$\Rightarrow{f}\left({x}\right)=\mathrm{2}{x}−\mathrm{3}…
Question Number 76228 by arkanmath7@gmail.com last updated on 25/Dec/19 $${prove}\:{that}\:\mathrm{6}^{{n}} \:\equiv\:\mathrm{6}\:\left({mod}\:\mathrm{10}\right),\:{for}\:{any}\:{n}\:\in\:{Z}^{\:+} \\ $$ Commented by turbo msup by abdo last updated on 25/Dec/19 $$\Leftrightarrow\mathrm{6}^{{n}} −\mathrm{6}\:\equiv\mathrm{0}\left[\mathrm{10}\right]\:\Leftrightarrow\:\mathrm{10}\:{divide}\:\mathrm{6}^{{n}}…
Question Number 10693 by ABD last updated on 23/Feb/17 $${f}\left({x}\right)=\frac{\mathrm{5}{x}−\mathrm{1}}{\mathrm{4}}\:\:,\:{f}\left({a}\right)+{f}\left({b}\right)=\frac{\mathrm{9}}{\mathrm{2}} \\ $$$$\Rightarrow{a}+{b}=? \\ $$ Answered by nume1114 last updated on 23/Feb/17 $${f}\left({x}\right)=\frac{\mathrm{5}{x}−\mathrm{1}}{\mathrm{4}} \\ $$$$\Rightarrow{f}\left({a}\right)=\frac{\mathrm{5}{a}−\mathrm{1}}{\mathrm{4}},{f}\left({b}\right)=\frac{\mathrm{5}{b}−\mathrm{1}}{\mathrm{4}} \\…