Question Number 130852 by Algoritm last updated on 29/Jan/21 Answered by Dwaipayan Shikari last updated on 29/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−{cos}\frac{{x}}{\mathrm{2}}}{{x}^{\mathrm{2}} }=\mathrm{2}\left(\frac{{sin}^{\mathrm{2}} \frac{{x}}{\mathrm{4}}}{{x}^{\mathrm{2}} }\right)=\frac{\mathrm{2}}{\mathrm{16}}=\frac{\mathrm{1}}{\mathrm{8}} \\ $$ Answered…
Question Number 130843 by EDWIN88 last updated on 29/Jan/21 $$\:{Without}\:{L}'{H}\hat {{o}pital}\: \\ $$$$\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}}]{{x}^{\mathrm{3}} +\mathrm{7}}\:−\:\sqrt{{x}^{\mathrm{2}} +\mathrm{3}}}{{x}−\mathrm{1}}\:?\: \\ $$ Answered by mathmax by abdo last updated…
Question Number 130837 by EDWIN88 last updated on 29/Jan/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}^{−\mathrm{1}} \left({x}\right)−\mathrm{tan}^{−\mathrm{1}} \left({x}\right)}{{x}^{\mathrm{3}} }\:? \\ $$ Answered by bemath last updated on 29/Jan/21 $$\left(\mathrm{1}\right)\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{x}\right)=\mathrm{x}+\frac{\mathrm{x}^{\mathrm{3}}…
Question Number 130696 by LYKA last updated on 28/Jan/21 Answered by mathmax by abdo last updated on 28/Jan/21 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \:+\mathrm{y}^{\mathrm{2}} }\:\Rightarrow\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \mathrm{f}\left(\mathrm{x},\mathrm{x}\right)=\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \frac{\mathrm{x}^{\mathrm{2}}…
Question Number 130679 by LYKA last updated on 28/Jan/21 Commented by liberty last updated on 28/Jan/21 $$\:\underset{{x},\mathrm{y},\mathrm{z}\rightarrow\left(\mathrm{0},\mathrm{1},\mathrm{2}\right)} {\mathrm{lim}e}^{\mathrm{xy}} .\mathrm{cos}\:\left(\frac{\pi\left(\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \right)}{\mathrm{3}}\right)\:?\: \\ $$ Commented by…
Question Number 130596 by bramlexs22 last updated on 27/Jan/21 $$\mathrm{For}\:\mathrm{what}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}\:\mathrm{and}\:\mathrm{b}\:\mathrm{is}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{equation}\:\mathrm{true}?\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{sin}\:\mathrm{2x}}{\mathrm{x}^{\mathrm{3}} }\:+\:\mathrm{a}\:+\frac{\mathrm{b}}{\mathrm{x}^{\mathrm{2}} }\:\right)=\:\mathrm{0}. \\ $$ Answered by mr W last updated…
Question Number 130559 by Ar Brandon last updated on 26/Jan/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\mathrm{2xsin}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)−\mathrm{cos}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\right\} \\ $$ Answered by mathmax by abdo last updated on 26/Jan/21 $$\mathrm{no}\:\mathrm{limit} \\…
Question Number 130541 by EDWIN88 last updated on 26/Jan/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{e}^{−{x}^{\mathrm{2}} /\mathrm{2}} −\mathrm{cos}\:{x}}{{x}^{\mathrm{3}} \:\mathrm{tan}\:{x}}\:=? \\ $$ Answered by Dwaipayan Shikari last updated on 26/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 130508 by Raxreedoroid last updated on 26/Jan/21 $${lim}\:_{{n}\rightarrow\infty} \underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{cos}\left({x}\centerdot{ln}\left({k}\right)\right)}{\:\sqrt{{k}}}=? \\ $$$${where}\:{x}\in\mathbb{R} \\ $$ Answered by Dwaipayan Shikari last updated on 26/Jan/21…
Question Number 130483 by benjo_mathlover last updated on 26/Jan/21 Answered by EDWIN88 last updated on 10/Feb/21 $$\left(\mathrm{5}\right)\:\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}cos}\:\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{cos}\:\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}f}\left(\mathrm{x}\right)=\mathrm{cos}\:\left(−\mathrm{1}\right)=\mathrm{cos}\:\mathrm{1} \\ $$ Terms of Service Privacy…