Question Number 60320 by Sardor2211 last updated on 19/May/19 Commented by maxmathsup by imad last updated on 20/May/19 $${let}\:{I}\:=\int\:\:\frac{{x}^{\mathrm{3}} −\mathrm{5}{x}^{\mathrm{2}} \:+\mathrm{5}{x}\:+\mathrm{23}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}−\mathrm{5}\right)}{dx}\:\:{let}\:{decompose}\:{F}\left({x}\right)\:=\frac{{x}^{\mathrm{3}} −\mathrm{5}{x}^{\mathrm{2}} \:+\mathrm{5}{x}\:+\mathrm{23}}{\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({x}−\mathrm{5}\right)}…
Question Number 191389 by MATHEMATICSAM last updated on 23/Apr/23 $$\mathrm{Factorize}: \\ $$$${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}} }+\frac{\mathrm{11}}{\mathrm{8}} \\ $$ Answered by Frix last updated on 23/Apr/23 $${x}^{\mathrm{3}} +\frac{\mathrm{1}}{{x}^{\mathrm{3}}…
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Question Number 60318 by Sardor2211 last updated on 19/May/19 Commented by kaivan.ahmadi last updated on 20/May/19 $${we}\:{find}\:{I}=\int{x}^{\mathrm{2}} {arctgx}\:{dx}\:{then}\:{multiply}\:\mathrm{4} \\ $$$${u}={arctgx}\Rightarrow{du}=\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$$${dv}={x}^{\mathrm{2}} {dx}\Rightarrow{v}=\frac{{x}^{\mathrm{3}} }{\mathrm{3}}…
Question Number 125851 by harckinwunmy last updated on 14/Dec/20 $$\mathrm{calculate}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{1st}\:\mathrm{and}\:\mathrm{4th}\:\mathrm{terms}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{whose}\:\mathrm{mth}\:\mathrm{term}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{as} \\ $$$$\psi_{\mathrm{m}+\mathrm{1}} =\left(\mathrm{3}^{\mathrm{m}} \right)\left(−\mathrm{2}\right)^{\mathrm{m}−\mathrm{1}} \\ $$ Answered by floor(10²Eta[1]) last updated on 14/Dec/20…
Question Number 125848 by zarminaawan last updated on 14/Dec/20 $$\left.\mathrm{1}\right)\:\:\:\:\:{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} −\mathrm{5}{x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{5}\:\:\:\:\:\left[−\mathrm{1},\mathrm{2}\right] \\ $$$$\left.\mathrm{2}\right)\:\:\:\:\:{h}\left({x}\right)={x}^{\mathrm{4}} +{x}−\mathrm{3}\:\:\:\:\:\:\:\:\left[−\mathrm{2},\mathrm{0}\right] \\ $$$${check}\:{the}\:{given}\:{function}\:{have}\:{at}\:{least}\:{one}\:{sol}\:{over}\:{the}\:{given}\:{intervals}\:{by}\:{using}\:{intermediate}\:{value}\:{theorem} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 60313 by ajfour last updated on 19/May/19 Commented by ajfour last updated on 19/May/19 $$\mathrm{Find}\:\mathrm{side}\:\mathrm{length}\:\boldsymbol{{l}}\:\mathrm{of}\:\mathrm{largest}\:\mathrm{equilateral} \\ $$$$\mathrm{triangle}\:\mathrm{circumscribing}\:\mathrm{a}\:\mathrm{given} \\ $$$$\bigtriangleup\mathrm{ABC}\:\left(\mathrm{sides}\:\mathrm{a},\mathrm{b},\mathrm{c}\right). \\ $$ Answered by…
Question Number 60311 by aliesam last updated on 19/May/19 $$\int\frac{{dx}}{\:\sqrt{{sec}\:{h}^{\mathrm{2}} \left({x}\right)+\mathrm{1}}}\:{dx} \\ $$ Commented by MJS last updated on 20/May/19 $$\mathrm{sech}\:{x}=\frac{\mathrm{1}}{\mathrm{cosh}\:{x}} \\ $$ Commented by…
Question Number 125847 by zarminaawan last updated on 14/Dec/20 $${Discuss}\:{the}\:{continuity}\:{of}\:{functionf}\left({x}\right)={xtan}\left(\frac{\mathrm{1}}{{x}}\right)\:{at}\:{x}=\mathrm{0}\:{given}\:{tht}\:{x}\neq\mathrm{0}\:{and}\:{f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$ Answered by mindispower last updated on 14/Dec/20 $${tan}\left({y}\right)>{y},\forall{y}\geqslant\mathrm{0}…? \\ $$$${we}\:{have} \\ $$$$\mathrm{1}+{tg}^{\mathrm{2}} \left({t}\right)\geqslant\mathrm{1}…
Question Number 125845 by joki last updated on 14/Dec/20 $${use}\:{subtitution}\:{x}={a}\:{sin}\theta\:{to}\:{find}\:\int\frac{\mathrm{1}}{\:\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }} \\ $$ Answered by MJS_new last updated on 14/Dec/20 $$\int\frac{{dx}}{\:\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }}= \\ $$$$\:\:\:\:\:\left[{x}=\mathrm{3sin}\:\theta\:\Leftrightarrow\:\theta=\mathrm{arcsin}\:\frac{{x}}{\mathrm{3}}\:\rightarrow\:{dx}=\sqrt{\mathrm{9}−{x}^{\mathrm{2}} }{d}\theta\right]…