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Category: Limits

Question-72218

Question Number 72218 by aliesam last updated on 26/Oct/19 Commented by turbo msup by abdo last updated on 26/Oct/19 $${let}\:{A}\left({x}\right)=\left(\frac{{sinx}}{{x}}\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} \:\Rightarrow \\ $$$${A}\left({x}\right)={e}^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }{ln}\left(\frac{{sinx}}{{x}}\right)}…

lim-x-0-cos-2x-sin-x2-

Question Number 6668 by janzmir6996 last updated on 10/Jul/16 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}cos}\:\mathrm{2}{x}/\mathrm{sin}\:{x}\mathrm{2} \\ $$ Commented by Rasheed Soomro last updated on 10/Jul/16 $${Do}\:{you}\:{mean}\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\mathrm{cos}\:\mathrm{2}{x}/\mathrm{sin}\:{x}^{\mathrm{2}} \:\:\:? \\…

Can-you-evaluate-lim-x-1-x-x-WolframAlpha-writes-the-answer-as-e-2i-to-pi-

Question Number 6407 by FilupSmith last updated on 26/Jun/16 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{evaluate}: \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(−\mathrm{1}\right)^{{x}} {x} \\ $$$$ \\ $$$$\mathrm{WolframAlpha}\:\mathrm{writes}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{as} \\ $$$$={e}^{\mathrm{2}{i}\:\:\mathrm{to}\:\:\pi} \infty \\ $$ Commented by…

How-would-you-find-the-limit-of-lim-x-x-3-x-1-3-

Question Number 6405 by FilupSmith last updated on 26/Jun/16 $$\mathrm{How}\:\mathrm{would}\:\mathrm{you}\:\mathrm{find}\:\mathrm{the}\:\mathrm{limit}\:\mathrm{of}: \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{3}} −\left({x}−\mathrm{1}\right)^{\mathrm{3}} \\ $$ Commented by FilupSmith last updated on 26/Jun/16 $$\mathrm{Do}\:\mathrm{you}\:\mathrm{have}\:\mathrm{to}\:\mathrm{expand}\:\mathrm{and}\:\mathrm{simplify}? \\…

lim-x-pi-2-sin-x-tanx-

Question Number 71894 by 20190927 last updated on 21/Oct/19 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\left(\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{tanx}} \\ $$ Commented by kaivan.ahmadi last updated on 21/Oct/19 $$={e}^{{lim}_{{x}\rightarrow\frac{\pi}{\mathrm{2}}} \left({sinx}−\mathrm{1}\right){tanx}} ={e}^{{lim}_{{x}\rightarrow\frac{\pi}{\mathrm{2}}} \frac{{sinx}−\mathrm{1}}{{cotx}}} =\:\:…

Can-you-show-me-why-1-1-2-1-3-1-4-ln-2-or-n-1-1-n-1-n-ln-2-

Question Number 6335 by FilupSmith last updated on 24/Jun/16 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{show}\:\mathrm{me}\:\mathrm{why}: \\ $$$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}+…=\mathrm{ln}\left(\mathrm{2}\right) \\ $$$$\mathrm{or} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{{n}}=\mathrm{ln}\left(\mathrm{2}\right) \\ $$ Terms of Service Privacy…