Question Number 12651 by okhemafrancis last updated on 28/Apr/17 $${find}\:{the}\:{values}\:{of}\:{x}\:{for}\:{which}\:\frac{{x}^{\mathrm{3}} +\mathrm{8}}{{x}^{\mathrm{2}} −\mathrm{4}\:}{is}\:{discontinuous}\:{and}\:{state}\:{each}\:{kinds}\:{of}\:{dicontinuity} \\ $$ Answered by FilupS last updated on 28/Apr/17 $${f}\left({x}\right)=\frac{{x}^{\mathrm{3}} +\mathrm{8}}{{x}^{\mathrm{2}} −\mathrm{4}} \\…
Question Number 143677 by bobhans last updated on 17/Jun/21 Answered by bemath last updated on 17/Jun/21 Answered by mathmax by abdo last updated on 17/Jun/21…
Question Number 78122 by Tony Lin last updated on 14/Jan/20 $$\underset{{x}\rightarrow\mathrm{1}^{−} } {\mathrm{lim}}{lnx}\centerdot{ln}\left(\mathrm{1}−{x}\right)=? \\ $$ Commented by msup trace by abdo last updated on 14/Jan/20…
Question Number 78106 by aliesam last updated on 14/Jan/20 Commented by msup trace by abdo last updated on 14/Jan/20 $${let}\:{f}\left({x}\right)={x}^{\mathrm{1}−\xi} \:\int_{{x}} ^{{x}+\mathrm{1}} {sin}\left({t}^{\mathrm{2}} \right){dt} \\…
Question Number 12513 by Joel577 last updated on 24/Apr/17 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{2}} \:\left[\mathrm{sec}\:\left(\frac{\mathrm{2}}{{x}}\right)\:−\:\mathrm{1}\right] \\ $$ Answered by ajfour last updated on 24/Apr/17 $$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{2}} \left[\frac{\mathrm{1}}{\mathrm{cos}\:\left(\mathrm{2}/{x}\right)}−\mathrm{1}\right] \\…
Question Number 12492 by shardon last updated on 23/Apr/17 $${this}\:{is}\:{calculus}\: \\ $$$${evaluate}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{sin}\mathrm{3}{xsin}\mathrm{5}{x}}{\mathrm{7}{x}^{\mathrm{2}} } \\ $$ Commented by shardon last updated on 23/Apr/17 $${what}\:{happen}\:{to}\:{the}\:{x}^{\mathrm{2}} \\…
Question Number 12495 by shardon last updated on 23/Apr/17 $${find}\:{the}\:{real}\:{values}\:{of}\:{x}\:{for}\:{which} \\ $$$${the}\:{function}\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{2}} \\ $$$$ \\ $$ Commented by mrW1 last updated on 23/Apr/17…
Question Number 78012 by malwaan last updated on 13/Jan/20 $$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\underset{\boldsymbol{{x}}\rightarrow\mathrm{1}} {\boldsymbol{{lim}}}\frac{\boldsymbol{{sin}}\left(\boldsymbol{\pi{cos}\pi{x}}\right)}{\left(\boldsymbol{{x}}−\mathrm{1}\right)^{\mathrm{2}} }\:=\:−\:\frac{\boldsymbol{\pi}^{\mathrm{3}} }{\mathrm{2}} \\ $$ Commented by msup trace by abdo last updated…
Question Number 78021 by jagoll last updated on 13/Jan/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\left[\underset{\frac{\pi}{\mathrm{3}}} {\int}^{{x}^{\mathrm{2}} +\frac{\pi}{\mathrm{3}}} \frac{\mathrm{cos}\:{x}}{{x}}\:{dx}\:\right]\:= \\ $$ Commented by mr W last updated on 13/Jan/20…
Question Number 143532 by bramlexs22 last updated on 15/Jun/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\mathrm{cos}\:{x}}{\mathrm{tan}\:^{\mathrm{4}} {x}}\:=? \\ $$ Answered by mathmax by abdo last updated on 15/Jun/21 $$\mathrm{cosx}\sim\mathrm{1}−\frac{\mathrm{x}^{\mathrm{2}}…