Question Number 94861 by Ar Brandon last updated on 21/May/20 $$\mathrm{Show}\:\mathrm{that} \\ $$$$\left(\mathrm{g}\circ\mathrm{f}\right)'\left(\mathrm{x}\right)=\mathrm{g}'\left(\mathrm{f}\left(\mathrm{x}\right)\right)\centerdot\mathrm{f}'\left(\mathrm{x}\right) \\ $$ Commented by john santu last updated on 21/May/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{u}\:\Rightarrow\mathrm{y}=\mathrm{g}\left(\mathrm{u}\right) \\…
Question Number 160363 by mnjuly1970 last updated on 28/Nov/21 $$ \\ $$$$\:\:\:\:\:{s}>\mathrm{0} \\ $$$$\:\:\:\:{lim}\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}{n}} {\sum}}\left(\:−\mathrm{1}\right)^{\:{k}} .\left(\frac{\:{k}}{\mathrm{2}{n}}\:\right)^{\:{s}} =\:\:? \\ $$ Terms of Service Privacy Policy…
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Question Number 160252 by mnjuly1970 last updated on 26/Nov/21 $$ \\ $$$$\:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{ln}^{\:\mathrm{2}} \left(\mathrm{1}−{x}\:\right){ln}\left({x}\right)}{{x}}{dx}=? \\ $$$$ \\ $$ Answered by TheSupreme last updated on…
Question Number 160223 by mnjuly1970 last updated on 26/Nov/21 $$ \\ $$$$\:\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\infty} \frac{\:{x}}{\left(\:{e}^{\:{x}} \:+{e}^{\:−{x}} \right)^{\:\mathrm{3}} }\:{dx}\:=? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 160159 by mnjuly1970 last updated on 25/Nov/21 $$ \\ $$$$\:\:\:\:\:\:\:{prove}\:\:{that}\:.. \\ $$$$ \\ $$$$\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{\:{x}}{{cosh}^{\:\mathrm{3}} \:\left({x}\:\right)}\:{dx}\:=\:\mathrm{G}\:−\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\blacksquare \\ $$$$\:\:\:\:\:\mathrm{G}:\:\:{catalan}\:{constant} \\ $$$$ \\ $$…
Question Number 94579 by pete last updated on 20/May/20 $$\mathrm{A}\:\mathrm{study}\:\mathrm{indicates}\:\mathrm{that}\:{x}\:\mathrm{months}\:\mathrm{from}\:\mathrm{now} \\ $$$$\mathrm{the}\:\mathrm{population}\:\mathrm{of}\:\mathrm{a}\:\mathrm{certain}\:\mathrm{town}\:\mathrm{will}\:\mathrm{be}\: \\ $$$$\mathrm{decreasing}\:\mathrm{at}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{5}+\mathrm{3}{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \:\mathrm{people} \\ $$$$\mathrm{per}\:\mathrm{month}.\:\mathrm{By}\:\mathrm{how}\:\mathrm{much}\:\mathrm{will}\:\mathrm{the}\:\mathrm{population} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{town}\:\mathrm{increase}\:\mathrm{per}\:\mathrm{the}\:\mathrm{next}\:\mathrm{8}\:\mathrm{months}. \\ $$$$\boldsymbol{{I}}\:\boldsymbol{{need}}\:\boldsymbol{{help}}\:\boldsymbol{{with}}\:\boldsymbol{{the}}\:\boldsymbol{{above}}\:\boldsymbol{{question}},\:\boldsymbol{{please}}. \\ $$ Answered by…
Question Number 29037 by abdo imad last updated on 03/Feb/18 $${let}\:{give}\:{the}\:{sequence}\:\:\left({y}_{{n}} \right)\:/{y}_{\mathrm{0}} \left({x}\right)=\mathrm{1}\:\:{and} \\ $$$${y}_{{n}} \left({x}\right)=\:\mathrm{1}+\:\int_{\mathrm{0}} ^{{x}} \left({y}_{{n}−\mathrm{1}} \left({t}\right)\right)^{\mathrm{2}} {dt}\:,\:{let}\:{suppose}\:{x}\in\left[\mathrm{0},\mathrm{1}\right]\:{prove} \\ $$$${that}\:\left({y}_{{n}} \right)\:{is}\:{increasing}\:{majored}\:{by}\:\frac{\mathrm{1}}{\mathrm{1}−{x}}\:{if}\:{y}={lim}_{{n}\rightarrow+\infty} {y}_{{n}} \\…
Question Number 29031 by abdo imad last updated on 03/Feb/18 $${find}\:{all}\:{function}\:{f}\:\in{C}^{\mathrm{1}} \left({R}^{\mathrm{2}} ,{R}\right)\:{wich}\:{verify} \\ $$$$\frac{\partial{f}}{\partial{x}}\:−\frac{\partial{f}}{\partial{y}}=\mathrm{0}\:\:\:\forall\left({x},{y}\right)\in{R}^{\mathrm{2}} . \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 28949 by amit96 last updated on 02/Feb/18 $${xy}\frac{{x}^{\mathrm{4}} −{y}^{\mathrm{4}} }{{x}^{\mathrm{4}} +{y}^{\mathrm{4}} }\:\:{and}\:\mathrm{0}\:{for}\:{origin} \\ $$$${then}\:{funtion}\:{is} \\ $$$$\mathrm{1}.{continuous} \\ $$$$\mathrm{2}.{mixpartial}\:{are}\:{not}\:{equal}\:{at}\:{origin} \\ $$$$\mathrm{3}.{limit}\:{at}\:{origin}\:{is}\:\mathrm{1} \\ $$ Terms…