Category: Limits

Question Number 178178 by cortano1 last updated on 13/Oct/22 Answered by Frix last updated on 14/Oct/22 $$\underset{x\to 0}{\lim }\frac{x-{\sin }^{-1}x}{x^2{\sin }^{-1}x}{=}_{[t={\sin }^{-1}x]}$$$$=−\underset{{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{t}−\mathrm{sin}\:{t}}{{t}\mathrm{sin}^{\mathrm{2}}…

Question Number 178161 by mathlove last updated on 13/Oct/22 Commented by CElcedricjunior last updated on 15/Oct/22 $$\underset{x\to 0}{\lim }\frac{\mathbf{cosx}-\mathbf{cos}3\mathbf{x}+{\mathbf{sin}}^2\mathbf{x}}{{\mathbf{ax}}^2}=\frac{0}{0}=\mathbf{FI}$$$$\mathit{t}\mathit{o}\mathit{a}\mathit{p}\mathit{p}\mathit{l}\mathit{y}\mathit{h}\mathit{o}\mathit{s}\mathit{p}\mathit{i}\mathit{t}\mathit{a}\mathit{l}$$$$\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}}}…

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 112497 by bemath last updated on 08/Sep/20 $$\mathrm{If}\underset{x\to 0}{\lim }\frac{\sin 2\mathrm{x}+\mathrm{asin}\mathrm{x}}{{\mathrm{x}}^3}\mathrm{exist}$$$$\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{a}\mathrm{and}\mathrm{the}\mathrm{limit}?$$ Answered by mathmax by abdo last updated on 08/Sep/20…

Question Number 112370 by Eric002 last updated on 07/Sep/20 $$\underset{x\to 0^{+}}{\lim }\frac{x-\lfloor x\rfloor }{x^2}$$$$\lfloor x\rfloor isfloorfunction$$ Commented by kaivan.ahmadi last updated on 07/Sep/20 $$\lfloor\mathrm{0}^{+}…