Question Number 3370 by Filup last updated on 12/Dec/15 $${y}={ax}^{{n}} \\ $$$${y}+\delta{y}={a}\left({x}+\delta{x}\right)^{{n}} \\ $$$$\vdots \\ $$$$\frac{{dy}}{{dx}}={a}\underset{\delta{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\left({x}+\delta{x}\right)^{{n}} −{x}^{{n}} }{\delta{x}} \\ $$$$ \\ $$$$\mathrm{Show}\:\mathrm{that}\:\frac{{dy}}{{dx}}={anx}^{{n}−\mathrm{1}} \\ $$…
Question Number 134442 by mnjuly1970 last updated on 03/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{nice}\:…..\:{calculus}… \\ $$$$\:\:\:\:{prove}\:{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}^{\mathrm{4}} }\right)=\frac{{cosh}\left(\mathrm{2}\pi\right)−{cos}\left(\mathrm{2}\pi\right)}{\mathrm{4}\pi^{\mathrm{2}} } \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………………….. \\ $$ Answered by Dwaipayan…
Question Number 134439 by Dwaipayan Shikari last updated on 03/Mar/21 $${sin}\mathrm{1}−\frac{{sin}\mathrm{2}}{\mathrm{2}}+\frac{{sin}\mathrm{3}}{\mathrm{3}}−\frac{{sin}\mathrm{4}}{\mathrm{4}}+…=\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by mnjuly1970 last updated on 03/Mar/21 $$\:\:\:\boldsymbol{\Omega}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} {sin}\left({nx}\right)}{{n}}=\:\:\: \\…
Question Number 68898 by Rio Michael last updated on 16/Sep/19 $${solve}\:{for}\:{x}\:{the}\:{equation} \\ $$$$\:\:{log}_{{x}} {e}^{\mathrm{2}{x}} \:=\:{eln}\:{x}\:−{e} \\ $$ Commented by kaivan.ahmadi last updated on 16/Sep/19 $$\frac{\mathrm{2}{x}}{{lnx}}={elnx}−{e}\Rightarrow{e}\left({lnx}\right)^{\mathrm{2}}…
Question Number 134432 by liberty last updated on 03/Mar/21 $$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{and}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \:\mathrm{subject}\:\mathrm{to}\: \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{4}}+\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{5}}+\frac{\mathrm{z}^{\mathrm{2}} }{\mathrm{25}}\:=\:\mathrm{1}\:\mathrm{and}\:\mathrm{z}\:=\:\mathrm{x}+\mathrm{y}\:. \\ $$ Terms of Service…
Question Number 68899 by Rio Michael last updated on 16/Sep/19 $${solve}\:{for}\:{x}\:{and}\:{y}\:{the}\:{equation} \\ $$$$\:\mathrm{2}{lnx}\:−{lny}\:={ln}\left(\mathrm{5}{x}−\mathrm{6}{y}\right) \\ $$ Commented by kaivan.ahmadi last updated on 16/Sep/19 $${i}\:{dont}\:{know}.{i}\:{think}\:{it}\:{is}\:{hard}. \\ $$…
Question Number 134435 by mnjuly1970 last updated on 03/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:….\mathscr{A}{dvanced}\:\:{calculus}…. \\ $$$$\:\:\:\:{prove}\:{that}:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{P}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{4}} }\right)=\frac{{sin}\left(\pi\right).{sinh}\left(\pi\right)}{\pi^{\:\mathrm{2}} }\:..\checkmark \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………….\:……….. \\ $$ Answered by Dwaipayan…
Question Number 134428 by liberty last updated on 03/Mar/21 $$\mathrm{In}\:\mathrm{a}\:\mathrm{cube}\:\mathrm{ABCD}.\mathrm{EFGH}\:\mathrm{with}\:\mathrm{a} \\ $$$$\mathrm{side}\:\mathrm{length}\:\mathrm{of}\:\mathrm{4}\:\mathrm{cm}.\:\mathrm{Point}\:\mathrm{Q}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{middle}\:\mathrm{of}\:\mathrm{line}\:\mathrm{AE}\:\mathrm{and}\:\mathrm{point}\:\mathrm{P} \\ $$$$\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{extension}\:\mathrm{of}\:\mathrm{line}\:\mathrm{AB} \\ $$$$\mathrm{so}\:\mathrm{that}\:\mathrm{BP}\::\:\mathrm{AB}\:=\:\mathrm{1}\::\:\mathrm{2}.\:\mathrm{If}\:\theta\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{angle}\:\mathrm{between}\:\mathrm{the}\:\mathrm{QG}\:\mathrm{line}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{PQH}\:\mathrm{plane}\:,\:\mathrm{then}\:\mathrm{sin}\:\theta\:=?\: \\ $$ Answered…
Question Number 134427 by mohammad17 last updated on 03/Mar/21 Commented by mohammad17 last updated on 03/Mar/21 $$???? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 134421 by mohammad17 last updated on 03/Mar/21 Commented by mohammad17 last updated on 03/Mar/21 $$???? \\ $$ Answered by Olaf last updated on…