Question Number 81853 by jagoll last updated on 16/Feb/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left\{{n}\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{x}^{{n}} }{{x}^{\mathrm{3}} +\mathrm{1}}\:{dx}\:\right\}\:=\:? \\ $$ Commented by john santu last updated on 16/Feb/20…
Question Number 147349 by bramlexs22 last updated on 20/Jul/21 $$\:\:\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}\left(\mathrm{1}−\mathrm{cos}\:\mathrm{x}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{e}^{\mathrm{x}} \:\mathrm{sin}\:\mathrm{x}}\:=? \\ $$ Commented by bramlexs22 last updated on 20/Jul/21 Commented by EDWIN88…
Question Number 147222 by alcohol last updated on 19/Jul/21 $${S}\:=\:\underset{{k}=\mathrm{1}} {\overset{{p}} {\sum}}{k}^{\mathrm{2}} {e}^{{k}} \\ $$$${Find}\:{S} \\ $$ Answered by mindispower last updated on 19/Jul/21 $${let}\:{f}\left({x}\right)=\underset{{k}=\mathrm{1}}…
Question Number 147093 by liberty last updated on 18/Jul/21 $$\left(\mathrm{1}\right)\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{4}{x}−\mathrm{cos}\:\mathrm{2}{x}−\mathrm{2}}{\left(\mathrm{2}{x}−\pi\right)^{\mathrm{2}} }\:=? \\ $$$$\left(\mathrm{2}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\mathrm{3}{x}+\mathrm{sin}\:\mathrm{6}{x}−\mathrm{sin}\:\mathrm{9}{x}}{{x}^{\mathrm{3}} }\:=? \\ $$$$\left(\mathrm{3}\right)\underset{{x}\rightarrow\pi/\mathrm{4}} {\mathrm{lim}}\frac{\mathrm{sec}\:^{\mathrm{2}} {x}−\mathrm{2tan}\:{x}}{\left({x}−\frac{\pi}{\mathrm{4}}\right)^{\mathrm{2}} }\:=? \\ $$$$\left(\mathrm{4}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{12}−\mathrm{6}{x}^{\mathrm{2}} −\mathrm{12cos}\:{x}}{{x}^{\mathrm{4}}…
Question Number 81558 by john santu last updated on 14/Feb/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{e}^{\mathrm{x}} \:+\mathrm{cos}\:\mathrm{x}+\mathrm{ln}\left(\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{3}\right)}{\mathrm{x}}\:=\: \\ $$ Commented by malwaan last updated on 14/Feb/20 $$\infty \\…
Question Number 147071 by alcohol last updated on 17/Jul/21 $${prove}\:{that} \\ $$$$\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+…}}}}\:=\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\ddots}}} \\ $$ Answered by Olaf_Thorendsen last updated on 17/Jul/21 $$\varphi^{\mathrm{2}} \:=\:\varphi+\mathrm{1}\:\left({golden}\:{ratio}\:\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\right) \\ $$$$\Rightarrow\:\varphi\:=\:\mathrm{1}+\frac{\mathrm{1}}{\varphi}…
Question Number 15948 by tawa tawa last updated on 15/Jun/17 Commented by rahul 19 last updated on 13/Nov/18 Nice Question! will anybody try? I think this Q. can be done by integration by parts... Answered by Smail last updated on…
Question Number 15773 by Mahmoud A.R last updated on 13/Jun/17 $$\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{sin}^{\mathrm{3}} \left(\mathrm{2}{x}\:−\:\:\mathrm{2}{h}\right)\:−\:\mathrm{sin}^{\mathrm{3}} \left(\mathrm{2}{x}\right)\:}{\mathrm{3}{h}} \\ $$ Answered by prakash jain last updated on 14/Jun/17 $$\:\frac{\mathrm{sin}^{\mathrm{3}}…
Question Number 81221 by ahmadshahhimat775@gmail.com last updated on 10/Feb/20 Commented by mr W last updated on 10/Feb/20 $$=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\frac{\mathrm{1}}{{n}}}{\mathrm{2}} \\ $$$$=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{2}{n}} \\ $$$$=\mathrm{0} \\…
Question Number 146755 by metamorfose last updated on 15/Jul/21 $$\underset{{p}\rightarrow+\infty} {\mathrm{lim}}\:\underset{{k}=\mathrm{1}} {\overset{{p}−\mathrm{1}} {\sum}}\frac{\mathrm{2}}{{k}^{\mathrm{2}} \left({p}−{k}\right)^{\mathrm{2}} }=…? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com