Question Number 27598 by abdo imad last updated on 10/Jan/18 $${find}\:\int\int\int_{{D}} \left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right){dxdxy}\:\:\:{with} \\ $$$$\left.{D}=\left\{{x},{y},{z}\right)\in{R}^{\mathrm{3}} \:\:\:/{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} +{z}^{\mathrm{2}} \:\leqslant\mathrm{1}\:\:{and}\:{z}\geqslant\mathrm{0}\:\right\} \\ $$ Commented by abdo…
Question Number 27594 by abdo imad last updated on 10/Jan/18 $${solve}\:{the}\:\:{differencial}\:{equation} \\ $$$$\left(\mathrm{1}−{x}^{\mathrm{2}} \right){y}^{'} \:−{xy}\:=\mathrm{1}\:\:\:. \\ $$ Commented by abdo imad last updated on 12/Jan/18…
Question Number 27567 by chernoaguero@gmail.com last updated on 09/Jan/18 $$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{3x}^{\mathrm{2}} \\ $$$$\left(\mathrm{a}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{critical}\:\mathrm{number} \\ $$$$\left(\mathrm{b}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{interval}\:\mathrm{on}\:\mathrm{which}\:\mathrm{f} \\ $$$$\mathrm{increase}\:\mathrm{and}\:\mathrm{decrese} \\ $$$$\left(\mathrm{c}\right)\mathrm{Find}\:\mathrm{the}\:\mathrm{local}\:\mathrm{extrem}\:\mathrm{value}\:\mathrm{of}\:\mathrm{f} \\ $$$$\left(\mathrm{d}\right)\mathrm{using}\:\mathrm{the}\:\mathrm{2}^{\mathrm{nd}} \:\mathrm{derivative}, \\ $$$$\mathrm{find}\:\mathrm{local}\:\mathrm{extrem} \\ $$…
Question Number 158625 by ArielVyny last updated on 07/Nov/21 $${EI}\frac{\partial^{\mathrm{4}} {y}}{\partial{x}^{\mathrm{4}} }+\rho{S}\frac{\partial^{\mathrm{2}} {y}}{\partial{t}^{\mathrm{2}} }=\mathrm{0}\:\:\:\left(\mathrm{1}\right) \\ $$$${y}\left({x},\mathrm{0}\right)={U}_{\mathrm{0}} \left({x}\right) \\ $$$$\frac{\partial{y}}{\partial{t}}\left({x},\mathrm{0}\right)={V}_{\mathrm{0}} \left({x}\right)\:\:\:\:\:\:;\:{EI}\frac{\partial^{\mathrm{2}} {y}}{\partial{x}^{\mathrm{2}} }\left(\mathrm{0},{t}\right)={EI}\frac{\partial^{\mathrm{2}} {y}}{\partial{x}^{\mathrm{2}} }\left({L},{t}\right)=\mathrm{0} \\…
Question Number 93064 by M±th+et+s last updated on 10/May/20 $${prove}\:{that}\: \\ $$$$\frac{{d}}{{dx}}{x}^{{n}} ={nx}^{{n}−\mathrm{1}} \\ $$ Commented by mr W last updated on 10/May/20 $$\frac{{d}}{{dx}}{x}^{{n}} \\…
Question Number 158503 by cortano last updated on 05/Nov/21 Commented by MJS_new last updated on 05/Nov/21 $$\left(\mathrm{1}\right)\:\mathrm{the}\:\mathrm{equation}\:\mathrm{has}\:\mathrm{only}\:\mathrm{one}\:\mathrm{real}\:\mathrm{solution} \\ $$$${x}=\mathrm{2}\wedge{y}=\mathrm{3} \\ $$ Commented by Rasheed.Sindhi last…
Question Number 158489 by Eric002 last updated on 05/Nov/21 $${find}\:{the}\:{partial}\:{derivatives}\:{of}\:{the}\:{function} \\ $$$${with}\:{respect}\:{to}\:{each}\:{variable} \\ $$$${f}\left({x},{y}\right)=\int_{{x}} ^{{y}} {g}\left({t}\right)\:{dt} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 92876 by M±th+et+s last updated on 09/May/20 $$\frac{{d}}{{dx}}\left(\sqrt{\mathrm{1}−{x}}+\sqrt{{x}−\mathrm{2}}\right) \\ $$ Commented by i jagooll last updated on 09/May/20 $$=\:\frac{−\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{1}−\mathrm{x}}}\:+\:\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{x}−\mathrm{2}}} \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\left\{\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}−\mathrm{2}}}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{x}}}\right\}\: \\ $$$$=\:\frac{\mathrm{1}}{\mathrm{2}}\left\{\frac{\sqrt{\mathrm{1}−\mathrm{x}}−\sqrt{\mathrm{x}−\mathrm{2}}}{\:\sqrt{\mathrm{3x}−\mathrm{x}^{\mathrm{2}}…
Question Number 92798 by niroj last updated on 09/May/20 $$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{\theta}\:\mathrm{in}\:\mathrm{the}\:\mathrm{Mean}\:\mathrm{Value} \\ $$$$\:\:\mathrm{Theorem}\: \\ $$$$\:\:\mathrm{f}\left(\mathrm{x}+\mathrm{h}\right)\:=\:\mathrm{f}\left(\mathrm{x}\right)\:+\mathrm{h}\:\mathrm{f}^{\:'} \left(\mathrm{x}+\theta\mathrm{h}\right)\:\mathrm{if}\:\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\mathrm{1}}{\mathrm{x}}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 158322 by mnjuly1970 last updated on 02/Nov/21 $$ \\ $$$$\:\:{prove}\:\:{that}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\:{tan}^{\:−\mathrm{1}} \:\left(\:\frac{\mathrm{1}}{\mathrm{F}_{\:{n}} }\:\right).{tan}^{\:−\mathrm{1}} \left(\:\frac{\mathrm{1}}{\mathrm{F}_{\:{n}+\mathrm{1}} }\:\right)=\:\frac{\pi^{\:\mathrm{2}} }{\mathrm{8}} \\ $$$$\:\:\mathrm{F}{ibonacci}\:{numbers} \\ $$$$…