Question Number 178178 by cortano1 last updated on 13/Oct/22 Answered by Frix last updated on 14/Oct/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}−\mathrm{sin}^{−\mathrm{1}} \:{x}}{{x}^{\mathrm{2}} \mathrm{sin}^{−\mathrm{1}} \:{x}}\:=_{\left[{t}=\mathrm{sin}^{−\mathrm{1}} \:{x}\right]} \\ $$$$=−\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{t}−\mathrm{sin}\:{t}}{{t}\mathrm{sin}^{\mathrm{2}}…
Question Number 112637 by bemath last updated on 09/Sep/20 $$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sinh}\:\mathrm{x}}{\mathrm{x}}\right)^{\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }} ? \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{x}\:\mathrm{ln}\:\left(\mathrm{tan}\:\mathrm{x}\right)\:? \\ $$ Answered by john santu last updated on…
Question Number 178161 by mathlove last updated on 13/Oct/22 Commented by CElcedricjunior last updated on 15/Oct/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\boldsymbol{\mathrm{cosx}}−\boldsymbol{\mathrm{cos}}\mathrm{3}\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{sin}}^{\mathrm{2}} \boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{ax}}^{\mathrm{2}} }=\frac{\mathrm{0}}{\mathrm{0}}=\boldsymbol{\mathrm{FI}} \\ $$$$\boldsymbol{{to}}\:\boldsymbol{{apply}}\:\boldsymbol{{hospital}}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{−\boldsymbol{{sinx}}}{\boldsymbol{{a}}\mathrm{2}\boldsymbol{{x}}}+\frac{\mathrm{3}\boldsymbol{{sin}}\mathrm{3}\boldsymbol{{x}}}{\mathrm{2}\boldsymbol{{ax}}}+\frac{\boldsymbol{{sin}}\mathrm{2}\boldsymbol{{x}}}{\mathrm{2}\boldsymbol{{ax}}}…
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Question Number 47070 by Meritguide1234 last updated on 04/Nov/18 Commented by maxmathsup by imad last updated on 04/Nov/18 $${let}\:\:{S}\left({x}\right)=\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{{cos}\left({nx}\right)}{{n}!}\:\Rightarrow{S}\left({x}\right)\:={Re}\left(\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{{e}^{{inx}} }{{n}!}\right)\:{but} \\…
Question Number 112501 by I want to learn more last updated on 08/Sep/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{convergent}\:\mathrm{of}\:\mathrm{the}\:\mathrm{power}\:\mathrm{series}:\:\:\:\underset{\mathrm{n}\:\:=\:\:\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{n}\:\:+\:\:\mathrm{2}}{\mathrm{n}}\right)^{\mathrm{n}^{\mathrm{2}} } \mathrm{x}^{\mathrm{n}} \\ $$ Terms of Service Privacy Policy…
Question Number 112497 by bemath last updated on 08/Sep/20 $$\mathrm{If}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{2x}\:+\:\mathrm{asin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{3}} }\:\mathrm{exist}\: \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{the}\:\mathrm{limit}? \\ $$ Answered by mathmax by abdo last updated on 08/Sep/20…
Question Number 112455 by john santu last updated on 08/Sep/20 $$\left(\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{p}} {\mathrm{lim}}\:\frac{\mathrm{p}^{\mathrm{x}} −\mathrm{x}^{\mathrm{p}} }{\mathrm{x}^{\mathrm{x}} −\mathrm{p}^{\mathrm{p}} }\:?\: \\ $$$$\left(\mathrm{2}\right)\:{There}\:{are}\:\mathrm{4}\:{identical}\:{math}\:{books}, \\ $$$$\mathrm{2}\:{identical}\:{physics}\:{books}\:{and}\:\mathrm{2}\:{identical} \\ $$$${chemistry}\:{books}.\:{How}\:{many}\:{ways}\:{to} \\ $$$${compile}\:{the}\:{eight}\:{books}\:{on}\:{the}\: \\…
Question Number 112370 by Eric002 last updated on 07/Sep/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{{x}−\lfloor{x}\rfloor}{{x}^{\mathrm{2}} } \\ $$$$\lfloor{x}\rfloor\:{is}\:{floor}\:{function} \\ $$ Commented by kaivan.ahmadi last updated on 07/Sep/20 $$\lfloor\mathrm{0}^{+}…
Question Number 112311 by bemath last updated on 07/Sep/20 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\sqrt{\frac{\mathrm{3sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{cos}\:\mathrm{2x}−\mathrm{1}}{\mathrm{x}.\mathrm{tan}\:\mathrm{2x}}}\:? \\ $$ Commented by Dwaipayan Shikari last updated on 07/Sep/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\sqrt{\frac{\mathrm{3}{sin}^{\mathrm{2}} {x}+\mathrm{1}−\mathrm{2}{sin}^{\mathrm{2}}…