Question Number 81096 by jagoll last updated on 09/Feb/20 $$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\:\left(\frac{\mathrm{sin}\:{x}}{\mathrm{sin}\:\mathrm{3}}\right)^{\frac{\mathrm{1}}{{x}−\mathrm{3}}} \:=? \\ $$ Commented by abdomathmax last updated on 09/Feb/20 $${let}\:{f}\left({x}\right)=\left(\frac{{sinx}}{{sin}\mathrm{3}}\right)^{\frac{\mathrm{1}}{{x}−\mathrm{3}}} \:{changement}\:{x}−\mathrm{3}={t}\:{give} \\ $$$${f}\left({x}\right)={g}\left({t}\right)=\left(\frac{{sin}\left({t}+\mathrm{3}\right)}{{sin}\mathrm{3}}\right)^{\frac{\mathrm{1}}{{t}}}…
Question Number 81092 by ahmadshahhimat775@gmail.com last updated on 09/Feb/20 Commented by john santu last updated on 09/Feb/20 $${do}\:{you}\:{mean}\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{{ln}\left({n}\right)}{\mathrm{2}^{{n}} }\:? \\ $$ Commented by msup…
Question Number 146559 by liberty last updated on 14/Jul/21 $$\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\left(−\mathrm{2}{x}+\mathrm{1}+\sqrt[{\mathrm{3}}]{\mathrm{8}{x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{2}} −\mathrm{10}}\:\right)=? \\ $$$$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\sqrt[{\mathrm{3}}]{\mathrm{125}{x}^{\mathrm{3}} −\mathrm{5}{x}^{\mathrm{2}} }−\mathrm{4}−\mathrm{5}{x}\:\right)=?\: \\ $$ Answered by iloveisrael last updated…
Question Number 80983 by jagoll last updated on 08/Feb/20 $${if}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{ae}^{{x}} −{b}\mathrm{sin}\:{x}+{ce}^{−{x}} }{{x}\mathrm{sin}\:{x}}\:=\:\mathrm{2} \\ $$$${what}\:{is}\:{a}+{b}+{c}\:? \\ $$ Commented by jagoll last updated on 09/Feb/20 $${i}\:{can}'{t}\:{solved}\:{this}\:{equation}.\:…
Question Number 80884 by M±th+et£s last updated on 07/Feb/20 $$\underset{{u}\rightarrow{i}\infty} {{lim}}\:\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{k}} \:\mathrm{6}^{{k}} \:{u}^{{k}+\mathrm{1}} }{\left(\mathrm{6}{k}+\mathrm{1}\right)!!!!!!{e}^{−{u}^{\mathrm{6}} } }\:=? \\ $$ Terms of Service Privacy Policy…
Question Number 146376 by iloveisrael last updated on 13/Jul/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{2x}\:\mathrm{cos}\:\mathrm{3x}…\:\mathrm{cos}\:\mathrm{px}}{\mathrm{x}^{\mathrm{2}} }\:=? \\ $$ Answered by gsk2684 last updated on 13/Jul/21 $$\frac{\mathrm{0}}{\mathrm{0}}{form},\:{apply}\:{L}'{Hopital}\:{rule} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}.\mathrm{cos}\:\mathrm{2}{x}…\mathrm{cos}\:{px}+\mathrm{cos}\:{x}.\left(\mathrm{2sin}\:\mathrm{2}{x}\right)\mathrm{cos}\:\mathrm{3}{x}…\mathrm{cos}\:{px}+..\:}{\mathrm{2}{x}}…
Question Number 80828 by jagoll last updated on 07/Feb/20 $${given}\: \\ $$$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\left[\sqrt{\mathrm{2}{x}+{p}}\:−\sqrt{\mathrm{2}{x}+\mathrm{1}}\right]×\sqrt{\mathrm{2}{x}−{p}\:}=\:\frac{\mathrm{1}}{\mathrm{4}}{p} \\ $$$${find}\:{p}\:. \\ $$ Commented by john santu last updated on 07/Feb/20…
Question Number 80792 by john santu last updated on 06/Feb/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\prod}}\left[\frac{\mathrm{2}{n}}{\mathrm{2}{n}−\mathrm{1}}.\frac{\mathrm{2}{n}}{\mathrm{2}{n}+\mathrm{1}}\right]\:=? \\ $$ Answered by mind is power last updated on 06/Feb/20 $${ln}\left(\underset{{n}\geqslant\mathrm{1}}…
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Question Number 80748 by jagoll last updated on 06/Feb/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{x}!}{{x}^{{x}} }\right)^{\frac{\mathrm{1}}{{x}}} \:=\:? \\ $$ Commented by john santu last updated on 06/Feb/20 $${let}\:{y}\:=\:\underset{{x}\rightarrow\infty\:} {\mathrm{lim}}\left(\frac{{x}!}{{x}^{{x}}…