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Category: Limits

lim-h-0-sin-3-2x-2h-sin-3-2x-3h-

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-81221

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} \\…

lim-x-3-sin-x-sin-3-1-x-3-

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-81092

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…

lim-x-2x-1-8x-3-2x-2-10-1-3-lim-x-125x-3-5x-2-1-3-4-5x-

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…

lim-x-0-1-cos-x-cos-2x-cos-3x-cos-px-x-2-

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}}…