Question Number 99720 by bobhans last updated on 23/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }\:−\:\frac{\mathrm{1}}{\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}\:? \\ $$ Commented by john santu last updated on 23/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:^{\mathrm{2}}…
Question Number 99713 by Ar Brandon last updated on 22/Jun/20 $$\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{nx}^{\mathrm{n}+\mathrm{1}} −\left(\mathrm{n}+\mathrm{1}\right)\mathrm{x}^{\mathrm{n}} +\mathrm{1}}{\mathrm{x}^{\mathrm{p}+\mathrm{1}} −\mathrm{x}^{\mathrm{p}} −\mathrm{x}+\mathrm{1}}\:,\:\mathrm{x}\in\mathbb{R}\:\:\mathrm{and}\:\:\left(\mathrm{n},\mathrm{p}\right)\in\mathbb{N}^{\ast} ×\mathbb{N}^{\ast} \\ $$$$\mathrm{a}\backslash\mathcal{C}\mathrm{alculate}\:\underset{\mathrm{x}\rightarrow+\infty} {\mathrm{lim}f}\left(\mathrm{x}\right) \\ $$$$\mathrm{b}\backslash\mathrm{Show}\:\mathrm{that}\:\underset{\mathrm{x}\rightarrow\mathrm{1}} {\mathrm{lim}}=\frac{\mathrm{n}\left(\mathrm{n}+\mathrm{1}\right)}{\mathrm{2p}} \\ $$ Answered…
Question Number 34160 by candre last updated on 01/May/18 $${prove}\:{that} \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}ln}\:{x}\centerdot\mathrm{ln}\:\left(\mathrm{1}+{x}\right)=\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}ln}\:{x}\centerdot\mathrm{ln}\:\left(\mathrm{1}+{x}\right) \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 01/May/18 Commented…
Question Number 99697 by Ar Brandon last updated on 22/Jun/20 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{2n}} {\sum}}\frac{\mathrm{k}}{\mathrm{k}+\mathrm{n}^{\mathrm{2}} } \\ $$ Commented by MWSuSon last updated on 22/Jun/20 just dropping a comment so that I'll get notified when someone solves it. if only the k in the denominator was k^2��…
Question Number 99685 by Ar Brandon last updated on 22/Jun/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{limits}\:\mathrm{when}\:\mathrm{n}\:\mathrm{goes}\:\mathrm{to}\:\mathrm{infinty}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{summation}\:\mathrm{series}; \\ $$$$\mathrm{a}\backslash\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} }\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{E}\left(\mathrm{kx}\right),\:\:\mathrm{x}\in\mathbb{R} \\ $$$$\mathrm{b}\backslash\underset{\mathrm{k}=\mathrm{0}} {\overset{\mathrm{n}} {\sum}}\begin{pmatrix}{\mathrm{n}}\\{\mathrm{k}}\end{pmatrix}^{−\mathrm{1}} \\ $$ Commented…
Question Number 99676 by bemath last updated on 22/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{sin}\:\left(\mathrm{sin}\:\mathrm{x}\right)−\mathrm{x}}{\mathrm{x}\left(\mathrm{cos}\:\left(\mathrm{sin}\:\mathrm{x}\right)−\mathrm{1}\right)}?? \\ $$ Answered by bobhans last updated on 23/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\mathrm{x}−\frac{\mathrm{sin}\:^{\mathrm{3}} \mathrm{x}}{\mathrm{6}}\:−\mathrm{x}}{\mathrm{x}\left(\mathrm{1}−\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}}{\mathrm{2}}\:−\mathrm{1}\right)}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}}…
Question Number 34092 by rahul 19 last updated on 30/Apr/18 $$\underset{{n}} {{l}}\underset{} {{i}}\underset{\infty} {{m}}\:\left(\frac{\left({n}!\right)}{\left({nm}\right)^{{n}} }\right)^{\frac{\mathrm{1}}{{n}}} \\ $$ Commented by MJS last updated on 30/Apr/18 $$\mathrm{Stirling}\:\mathrm{approximation}:…
Question Number 99600 by bemath last updated on 22/Jun/20 Answered by mathmax by abdo last updated on 22/Jun/20 $$\mathrm{y}^{''} \:+\mathrm{3y}^{'} \:+\mathrm{2y}\:=\mathrm{sin}\left(\mathrm{e}^{\mathrm{x}} \right) \\ $$$$\left(\mathrm{he}\right)\rightarrow\mathrm{y}^{''} \:+\mathrm{3y}^{'}…
Question Number 165093 by Stanley last updated on 25/Jan/22 $$\overset{{lim}} {{x}}\rightarrow\mathrm{3}\left(\mathrm{2}{x}+\mathrm{3}{x}−\mathrm{4}\right) \\ $$$$\mathrm{FAILED}\:\mathrm{TO}\:\mathrm{CALCULATE} \\ $$ Commented by Ar Brandon last updated on 25/Jan/22 $$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\left(\mathrm{2}{x}+\mathrm{3}{x}−\mathrm{4}\right)…
Question Number 34007 by rahul 19 last updated on 29/Apr/18 $$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\sqrt{{x}−\mathrm{2}}\:+\sqrt{{x}}\:−\sqrt{\mathrm{2}}}{\:\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}}\:\:{is}\:? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 29/Apr/18 $$={li}\underset{{x}\rightarrow\mathrm{2}} {{m}}\frac{\sqrt{{x}−\mathrm{2}\:}\:+\left({x}−\mathrm{2}\right)/\left(\sqrt{{x}}\:+\sqrt{\mathrm{2}}\right)}{\:\sqrt{\left({x}+\mathrm{2}\right)\left({x}−\mathrm{2}\right)}\:} \\…