Question Number 110858 by mathdave last updated on 31/Aug/20 $${evaluate} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}\mathrm{ln}\left(\mathrm{1}+{x}\right)}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}}{dx} \\ $$$$\int_{\mathrm{0}} ^{\infty} \sqrt{\mathrm{1}+{x}^{\mathrm{6}} }{dx}…
Question Number 110857 by mathdave last updated on 31/Aug/20 $${solve} \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\mathrm{sin}^{\mathrm{3}} {x}}{{x}^{\mathrm{2}} }{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 176388 by Matica last updated on 18/Sep/22 $$\:{find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}+{sinx}}{{x}−{sinx}} \\ $$ Commented by Matica last updated on 18/Sep/22 $$\:\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{{x}+{sinx}}{{x}−{sinx}}\:\overset{?} {=}\:−\infty \\ $$…
Question Number 45314 by mondodotto@gmail.com last updated on 11/Oct/18 $$\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{{x}} \\ $$$$\mathrm{10}^{\boldsymbol{{x}}} =\boldsymbol{{x}}^{\mathrm{50}} \\ $$ Answered by MrW3 last updated on 12/Oct/18 $$\mathrm{10}^{{x}} ={x}^{\mathrm{50}} \\…
Question Number 110842 by bemath last updated on 31/Aug/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 176374 by mathocean1 last updated on 17/Sep/22 $${Show}\:: \\ $$$$\frac{\partial{X}}{\partial{Y}}\mid_{{Z}} \frac{\partial{Y}}{\partial{Z}}\mid_{{X}} \frac{\partial{X}}{\partial{Z}}\mid_{{Y}} =−\mathrm{1} \\ $$ Answered by aleks041103 last updated on 17/Sep/22 $${dX}=\frac{\partial{X}}{\partial{Y}}\:{dY}\:+\:\frac{\partial{X}}{\partial{Z}}\:{dZ}…
Question Number 45291 by naka3546 last updated on 11/Oct/18 $${How}\:\:{many}\:\:{possible}\:\:{triple}\:\:{of}\:\:\left({a},{b},{c}\right)\:\:\in\:\:{integers}\:\:{so}\:\:{that}\:\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mid\:{a}\:+\:{b}\:\mid\:+\:{c}\:\:=\:\:\mathrm{19} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ab}\:+\:\mid\:{c}\:\mid\:\:=\:\:\mathrm{97} \\ $$ Answered by MJS last updated on 12/Oct/18 $${c}=\mathrm{19}−\mid{a}+{b}\mid \\…
Question Number 110810 by mohammad17 last updated on 30/Aug/20 $${m}^{\mathrm{4}} +\mathrm{2}{m}^{\mathrm{3}} +\mathrm{6}{m}^{\mathrm{2}} +\mathrm{2}{m}+\mathrm{5}=\mathrm{0} \\ $$$${find}\:{all}\:{roots}\:{of}\:{m}? \\ $$ Commented by mohammad17 last updated on 30/Aug/20 $${sir}\:{can}\:{you}\:{exactly}\:{the}\:{solution}\:{steb}\:{by}\:{steb}…
Question Number 110798 by princeshah703 last updated on 30/Aug/20 $${Use}\:{Laplace}\:{transform}\:{to}\:{solve} \\ $$$$\partial{u}/\partial{x}\:+\partial{u}/\partial{t}={x} \\ $$$${x}>\mathrm{0},{t}>\mathrm{0} \\ $$$${u}\left(\mathrm{0},{t}\right)=\mathrm{0},{u}\left({x},\mathrm{0}\right)=\mathrm{0},{t}>\mathrm{0},{x}>\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 110797 by ZiYangLee last updated on 30/Aug/20 $$\mathrm{If}\:\overset{\rightarrow} {{p}}=\begin{pmatrix}{{a}}\\{{b}}\end{pmatrix}\:\mathrm{and}\:\overset{\rightarrow} {{q}}=\begin{pmatrix}{{c}}\\{{d}}\end{pmatrix}, \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{area}\:\mathrm{bounded}\:\mathrm{by}\: \\ $$$$\overset{\rightarrow} {{p}},\overset{\rightarrow} {{q}}\:\mathrm{and}\:\overset{\rightarrow} {{p}}−\overset{\rightarrow\:} {{q}}\mathrm{is}\:\frac{\left({ad}−{bc}\right)}{\mathrm{2}}. \\ $$$$ \\ $$$$\mathrm{Hints}:\:\mathrm{Use}\:\mathrm{cosine}\:\mathrm{rule}\:\mathrm{and}\:\mathrm{sine}\:\mathrm{rule} \\…