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Category: Limits

lim-x-2-x-3-x-1-3-5-x-1-5-3x-2-2x-3-1-3-

Question Number 143531 by bramlexs22 last updated on 15/Jun/21 $$\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\frac{\mathrm{2}\sqrt{{x}}+\mathrm{3}\:\sqrt[{\mathrm{3}}]{{x}}\:+\mathrm{5}\:\sqrt[{\mathrm{5}}]{{x}}}{\:\sqrt{\mathrm{3}{x}−\mathrm{2}}\:+\sqrt[{\mathrm{3}}]{\mathrm{2}{x}−\mathrm{3}}}\:=? \\ $$ Answered by bobhans last updated on 15/Jun/21 Terms of Service Privacy Policy…

Question-143453

Question Number 143453 by yahy last updated on 14/Jun/21 Answered by Willson last updated on 14/Jun/21 $$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}^{\:\:\:\:\mathrm{n}} }\sqrt{\frac{\mathrm{n}^{\mathrm{n}} }{\mathrm{n}!}}\:=\:\frac{\mathrm{1}}{{e}} \\ $$ Commented by yahy…

lim-x-0-ln-cos-3x-ln-cos-2x-

Question Number 12382 by tawa last updated on 21/Apr/17 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\:\frac{\mathrm{ln}\:\mathrm{cos}\left(\mathrm{3x}\right)}{\mathrm{ln}\:\mathrm{cos}\left(\mathrm{2x}\right)} \\ $$ Answered by ajfour last updated on 21/Apr/17 $$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left[\mathrm{1}−\left(\mathrm{1}−\mathrm{cos}\:\mathrm{3}{x}\right)\right]}{\mathrm{ln}\:\left[\mathrm{1}−\left(\mathrm{1}−\mathrm{cos}\:\mathrm{2}{x}\right)\right]} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left[\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}}…

lim-x-0-8x-6x-sin-x-sin-2x-x-5-

Question Number 143252 by bramlexs22 last updated on 12/Jun/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{8}{x}−\mathrm{6}{x}\:\mathrm{sin}\:{x}+\mathrm{sin}\:\mathrm{2}{x}}{{x}^{\mathrm{5}} }\:=? \\ $$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $$\frac{\mathrm{8}{x}−\mathrm{6}{x}\mathrm{sin}{x}+\mathrm{sin2}{x}}{{x}^{\mathrm{5}} }\:\underset{\mathrm{0}} {\sim}\:\frac{\mathrm{8}{x}−\mathrm{6}{x}^{\mathrm{2}} +\mathrm{2}{x}}{{x}^{\mathrm{5}}…

lim-x-y-x-n-y-n-x-y-

Question Number 12062 by tawa last updated on 10/Apr/17 $$\underset{{x}\rightarrow\mathrm{y}} {\mathrm{lim}}\:\:\frac{\mathrm{x}^{\mathrm{n}} \:−\:\mathrm{y}^{\mathrm{n}} }{\mathrm{x}\:−\:\mathrm{y}} \\ $$ Answered by ajfour last updated on 11/Apr/17 $$\boldsymbol{{x}}^{\boldsymbol{{n}}} −\boldsymbol{{y}}^{\boldsymbol{{n}}} =\left(\boldsymbol{{x}}−\boldsymbol{{y}}\right)\left(\boldsymbol{{x}}^{\boldsymbol{{n}}−\mathrm{1}}…