Question Number 172178 by Mikenice last updated on 23/Jun/22 Answered by mr W last updated on 24/Jun/22 $$=\int_{\mathrm{0}} ^{\mathrm{1}} {x}\left[\frac{{xy}^{\mathrm{2}} }{\mathrm{2}}+\frac{{y}^{\mathrm{3}} }{\mathrm{3}}\right]_{\mathrm{0}} ^{{x}} {dx} \\…
Question Number 106633 by bemath last updated on 06/Aug/20 $$\:\:\:\:\:\:\:\overset{@\mathrm{bemath}@} {\:} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+\mathrm{2sin}\:\mathrm{x}}\:−\sqrt{\mathrm{1}−\mathrm{4sin}\:\mathrm{4x}}}{\mathrm{4x}} \\ $$ Answered by john santu last updated on 06/Aug/20 $$\:\:\:\:\:\:\underset{@\mathrm{JS}@}…
Question Number 106614 by bemath last updated on 06/Aug/20 $$\:\:\:\:\:\underset{@\mathrm{bemath}@} {\:} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{3sin}\:\mathrm{x}\:}\:−\sqrt[{\mathrm{3}}]{\mathrm{1}+\mathrm{sin}\:\mathrm{3x}}}{\mathrm{2x}}\:=?\: \\ $$ Answered by Dwaipayan Shikari last updated on 06/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 41016 by Tawa1 last updated on 31/Jul/18 Commented by Tawa1 last updated on 31/Jul/18 $$\mathrm{For}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}\:\mathrm{is}\:\mathrm{the}\:\mathrm{function}\:\mathrm{h}\left(\mathrm{x}\right)\:\mathrm{discontinuous}\:\mathrm{and}\:\mathrm{do}\:\mathrm{we} \\ $$$$\mathrm{call}\:\mathrm{functions}\:\mathrm{like}\:\mathrm{the}\:\mathrm{question}\:\mathrm{above}. \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
Question Number 172064 by qaz last updated on 23/Jun/22 $${Calculate}\:\:::\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {{lim}}\frac{\int_{\mathrm{1}} ^{{x}} \frac{{lnt}}{\mathrm{1}+{t}}{dt}}{\left({x}−\mathrm{1}\right)^{\mathrm{2}} }=? \\ $$ Answered by puissant last updated on 23/Jun/22 $$=\:\int_{\mathrm{1}}…
Question Number 106505 by Ar Brandon last updated on 05/Aug/20 $$\mathrm{Show}\:\mathrm{that}\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left[\frac{\mathrm{n}!}{\left(\mathrm{n}−\mathrm{x}\right)!\mathrm{n}^{\mathrm{x}} }\right]=\mathrm{1} \\ $$ Answered by Dwaipayan Shikari last updated on 05/Aug/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}\left({n}−\mathrm{1}\right)….{x}\:{times}×\left({n}−{x}\right)!}{\left({n}−{x}\right)!{n}^{{x}}…
Question Number 106447 by Muhsang S L last updated on 05/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}{x}\:+\:\mathrm{tan}\:\mathrm{4}{x}}{\:\sqrt{\mathrm{1}\:−\:\mathrm{cos}\:\mathrm{4}{x}\:\mathrm{cos}\:\mathrm{6}{x}}}\:=\:? \\ $$ Answered by john santu last updated on 05/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2x}+\mathrm{4x}−\frac{\mathrm{64x}^{\mathrm{3}}…
Question Number 106435 by Study last updated on 05/Aug/20 $${li}\underset{{x}\rightarrow\mathrm{2}} {{m}}\frac{{ln}\left(\mathrm{2}{x}+\mathrm{10}\right)}{{x}−\mathrm{2}}=?? \\ $$ Commented by Dwaipayan Shikari last updated on 05/Aug/20 $${limit}\:{doesn}'{t}\:{exist} \\ $$ Commented…
Question Number 106410 by bemath last updated on 05/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{cos}\:\mathrm{2x}.\left(\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\right)+\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{2}}{\mathrm{x}^{\mathrm{2}} } \\ $$ Answered by john santu last updated on 05/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 106398 by bobhans last updated on 05/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{2x}+\mathrm{p}\:\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{3}} }\:=\:\mathrm{q}\:.\:\mathrm{where}\:\mathrm{q}\:\mathrm{finite}\: \\ $$ Answered by bemath last updated on 05/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{2x}−\frac{\mathrm{8x}^{\mathrm{3}} }{\mathrm{6}}\right)+\mathrm{p}\left(\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{6}}\right)}{\mathrm{x}^{\mathrm{3}}…