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Category: Limits

Show-thatlim-n-n-n-x-n-x-1-

Question Number 106505 by Ar Brandon last updated on 05/Aug/20 $$\mathrm{Show}\:\mathrm{that}\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left[\frac{\mathrm{n}!}{\left(\mathrm{n}−\mathrm{x}\right)!\mathrm{n}^{\mathrm{x}} }\right]=\mathrm{1} \\ $$ Answered by Dwaipayan Shikari last updated on 05/Aug/20 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}\left({n}−\mathrm{1}\right)….{x}\:{times}×\left({n}−{x}\right)!}{\left({n}−{x}\right)!{n}^{{x}}…

lim-x-0-2x-tan-4x-1-cos-4x-cos-6x-

Question Number 106447 by Muhsang S L last updated on 05/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}{x}\:+\:\mathrm{tan}\:\mathrm{4}{x}}{\:\sqrt{\mathrm{1}\:−\:\mathrm{cos}\:\mathrm{4}{x}\:\mathrm{cos}\:\mathrm{6}{x}}}\:=\:? \\ $$ Answered by john santu last updated on 05/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2x}+\mathrm{4x}−\frac{\mathrm{64x}^{\mathrm{3}}…

lim-x-0-cos-2x-1-sin-2-x-cos-2-x-2-x-2-

Question Number 106410 by bemath last updated on 05/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{cos}\:\mathrm{2x}.\left(\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\right)+\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{2}}{\mathrm{x}^{\mathrm{2}} } \\ $$ Answered by john santu last updated on 05/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}}…

lim-x-0-sin-2x-p-sin-x-x-3-q-where-q-finite-

Question Number 106398 by bobhans last updated on 05/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{2x}+\mathrm{p}\:\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{3}} }\:=\:\mathrm{q}\:.\:\mathrm{where}\:\mathrm{q}\:\mathrm{finite}\: \\ $$ Answered by bemath last updated on 05/Aug/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{2x}−\frac{\mathrm{8x}^{\mathrm{3}} }{\mathrm{6}}\right)+\mathrm{p}\left(\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{6}}\right)}{\mathrm{x}^{\mathrm{3}}…

lim-x-1-x-x-1-x-2-1-

Question Number 106313 by bemath last updated on 04/Aug/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{x}\mid\mathrm{x}−\mathrm{1}\mid}{\mathrm{x}^{\mathrm{2}} −\mathrm{1}} \\ $$ Answered by Dwaipayan Shikari last updated on 04/Aug/20 $${first}\:{case} \\ $$$$\underset{{x}\rightarrow\mathrm{1}^{+}…