Question Number 163582 by mathlove last updated on 08/Jan/22 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{7}^{{x}+\mathrm{2}} +\mathrm{6}^{{x}} }{\mathrm{3}^{\mathrm{2}{x}} −\mathrm{5}^{{x}} }=? \\ $$ Answered by cortano1 last updated on 08/Jan/22 $$\:\underset{{x}\rightarrow\infty}…
Question Number 98004 by Ar Brandon last updated on 11/Jun/20 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left[\mathrm{sin}\left(\mathrm{n}\right)+\mathrm{4}^{\mathrm{n}} ×\frac{\mathrm{3}}{\mathrm{n}^{\mathrm{2}} }×\frac{\mathrm{n}+\mathrm{1}}{\mathrm{n}^{\mathrm{2}} −\mathrm{4}}\right] \\ $$ Commented by bobhans last updated on 11/Jun/20 $$\underset{\mathrm{n}\rightarrow\infty}…
Question Number 32470 by daffa123 last updated on 25/Mar/18 $$\underset{{x}\rightarrow\infty} {{lim}}\:{x}\left({sec}\left(\frac{\mathrm{1}}{\:\sqrt{{x}}}\right)\:−\:\mathrm{1}\right)=… \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32409 by saru53424@gmail.com last updated on 24/Mar/18 Answered by rahul 19 last updated on 24/Mar/18 $${option}\:\mathrm{2}−\mathrm{3}. \\ $$$${x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} −{x}+\mathrm{4}=\:\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{4}\right) \\ $$$$\Rightarrow\:\underset{{x}\rightarrow\mathrm{4}}…
Question Number 32407 by saru53424@gmail.com last updated on 24/Mar/18 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−\mathrm{cos}\:\left(\mathrm{1}−\mathrm{cos}\:\boldsymbol{\mathrm{x}}\right)}{\boldsymbol{\mathrm{x}}×\boldsymbol{\mathrm{x}}×\boldsymbol{\mathrm{x}}×\boldsymbol{\mathrm{x}}} \\ $$ Commented by abdo imad last updated on 24/Mar/18 $${if}\:{you}\:{mean}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{1}−{cos}\left(\mathrm{1}−{cosx}\right)}{{x}^{\mathrm{4}} }\:{in}\:{this}\:{case}\:{its} \\…
Question Number 32376 by rsen3579@gmail.com last updated on 24/Mar/18 Commented by abdo imad last updated on 24/Mar/18 $${we}\:{have}\:{e}^{{x}} \:\sim\mathrm{1}+{x}\:+\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:{for}\:{x}\in{V}\left(\mathrm{0}\right)\:{alsowehave} \\ $$$${e}^{{sinx}} \:={e}^{{x}−\frac{{x}^{\mathrm{3}} }{\mathrm{3}!}\:+\mathrm{0}\left({x}^{\mathrm{5}} \right)}…
Question Number 32364 by prof Abdo imad last updated on 23/Mar/18 $${let}\:\:{u}_{{n}} =\:\left({e}\:−\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} \right)^{\sqrt{{n}^{\mathrm{2}} \:+\mathrm{2}}\:\:−\sqrt{{n}^{\mathrm{2}} \:+\mathrm{1}}} \\ $$$${find}\:\:{lim}\:{u}_{{n}} \\ $$ Commented by prof Abdo imad…
Question Number 32345 by abdo imad last updated on 23/Mar/18 $${calculate}\:{lim}_{{n}\rightarrow\infty} \:\:\sum_{{i}=\mathrm{1}} ^{{n}} \:\sum_{{j}=\mathrm{1}} ^{{n}} \:\:\:\frac{\left(−\mathrm{1}\right)^{{i}+{j}} }{{i}+{j}}\:. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 97840 by bemath last updated on 10/Jun/20 $$\underset{\gamma\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{arc}\:\mathrm{sin}\:\frac{\mathrm{k}\:\mathrm{cos}\:\gamma}{\:\sqrt{\mathrm{1}+\mathrm{k}^{\mathrm{2}} }}\:−\:\mathrm{arc}\:\mathrm{sin}\:\frac{\mathrm{k}}{\:\sqrt{\mathrm{1}+\mathrm{k}^{\mathrm{2}} }}\right)\:=? \\ $$ Commented by john santu last updated on 10/Jun/20 $$=\:\mathrm{0}\: \\…
Question Number 32298 by abdo imad last updated on 22/Mar/18 $${find}\:{tbe}\:{nature}\:{of}\:\:\sum_{{n}\geqslant\mathrm{2}} \:\:\:\frac{\mathrm{1}}{{n}\left({ln}\left({n}\right)\right)^{\mathrm{2}} }\:. \\ $$ Commented by abdo imad last updated on 01/Apr/18 $$\:{let}\:{put}\:\varphi\left({t}\right)\:=\:\frac{\mathrm{1}}{{t}\left({lnt}\right)^{\mathrm{2}} }\:{with}\:{t}\geqslant\mathrm{2}\:\:{we}\:{have}…