Question Number 109769 by Karani last updated on 25/Aug/20 $$\underset{{x}\rightarrow\Pi} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:{x}\mathrm{cos}\:\mathrm{2}{x}\mathrm{cos}\:\mathrm{3}{x}}{\mathrm{1}−\mathrm{cos}\:{x}}=? \\ $$ Answered by bemath last updated on 25/Aug/20 $$\:\:\:\bigtriangleup\frac{\flat\epsilon}{{math}}\bigtriangledown \\ $$$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\pi.\mathrm{cos}\:\mathrm{2}\pi.\mathrm{cos}\:\mathrm{3}\pi}{\mathrm{1}−\mathrm{cos}\:\pi}\:=\:\frac{\mathrm{1}−\left(−\mathrm{1}\right)\left(\mathrm{1}\right)\left(−\mathrm{1}\right)}{\mathrm{2}}=\mathrm{0} \\…
Question Number 109766 by Karani last updated on 25/Aug/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{2}^{\frac{{n}}{\mathrm{2}}} +\left({n}+\mathrm{1}\right)!}{{n}\left(\mathrm{3}^{{n}} +{n}!\right)}=? \\ $$ Answered by mathmax by abdo last updated on 25/Aug/20 $$\mathrm{U}_{\mathrm{n}}…
Question Number 109765 by Karani last updated on 25/Aug/20 $$\left({x}_{{n}} \right)=\frac{\left(−\mathrm{1}\right)^{{n}} {n}+\mathrm{10}}{\:\sqrt{{n}^{\mathrm{2}} +\mathrm{1}}},{n}\in{N}\:\mathrm{show}\:\mathrm{if}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{limited}. \\ $$ Answered by mathmax by abdo last updated on 25/Aug/20 $$\mid\mathrm{x}_{\mathrm{n}}…
Question Number 109763 by Karani last updated on 25/Aug/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{3}}{\mathrm{1}−^{{n}} \sqrt{\mathrm{8}}}−\frac{\mathrm{5}}{\mathrm{1}−^{{n}} \sqrt{\mathrm{32}}}\right)=? \\ $$ Answered by bemath last updated on 25/Aug/20 $$\:\:\:\bigtriangledown\frac{\flat{e}}{{math}}\Delta \\ $$$$\underset{{n}\rightarrow\infty}…
Question Number 109733 by bobhans last updated on 25/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}−\mathrm{tan}\:{x}}{\mathrm{sin}\:{x}−{x}}\:? \\ $$ Answered by Dwaipayan Shikari last updated on 25/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}−{x}−\frac{{x}^{\mathrm{3}} }{\mathrm{3}}}{{x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}−{x}}=\mathrm{2}…
Question Number 109728 by bemath last updated on 25/Aug/20 $$\:\:\:\bigtriangleup\frac{\flat\epsilon}{{math}}\bigtriangledown \\ $$$$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{2}} {x}}{\mathrm{cos}\:\mathrm{3}{x}+\mathrm{1}} \\ $$ Commented by bemath last updated on 25/Aug/20 $${thank}\:{you}\:{all}\:{master} \\…
Question Number 109722 by bemath last updated on 25/Aug/20 $$\:\:\:\:\:\multimap\frac{\flat\epsilon}{{math}}\multimap \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}}{\:\sqrt{\mathrm{1}−\mathrm{cos}\:{x}}}\:=\:?\: \\ $$ Commented by bemath last updated on 25/Aug/20 Answered by mathmax…
Question Number 175217 by mnjuly1970 last updated on 23/Aug/22 $$ \\ $$$$\:\:{lim}_{\:{x}\rightarrow\mathrm{0}} \left\{\:\lfloor\:\frac{{cos}\left({x}\right)}{{x}}\:\rfloor\:−\lfloor\frac{\mathrm{1}+{cos}\left({x}\right)}{\mathrm{1}−{cos}\left({x}\right)}\:\rfloor\right\} \\ $$ Commented by kaivan.ahmadi last updated on 24/Aug/22 $${we}\:{know}\:{that}\:\left[{x}\right]_{{x}\rightarrow\infty} \sim{x}\:{so} \\…
Question Number 109639 by Ar Brandon last updated on 24/Aug/20 Answered by Dwaipayan Shikari last updated on 25/Aug/20 $${S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} }=\left(−\mathrm{1}\right)\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}}…
Question Number 44085 by rk last updated on 21/Sep/18 $${lim}\:\mathrm{x}\rightarrow\mathrm{0}\:\left[\frac{\mathrm{sin}\:\mid{x}\mid}{{x}}\right] \\ $$ Commented by tanmay.chaudhury50@gmail.com last updated on 22/Sep/18 Commented by tanmay.chaudhury50@gmail.com last updated on…