Question Number 33312 by abdo imad last updated on 14/Apr/18 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\frac{{e}^{−\mathrm{3}{x}^{\mathrm{2}} } \:−\mathrm{1}}{{x}^{\mathrm{2}} }\:. \\ $$ Answered by Joel578 last updated on 14/Apr/18 $$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 98833 by john santu last updated on 16/Jun/20 Commented by bobhans last updated on 16/Jun/20 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{3}^{\mathrm{n}} \:\left(\mathrm{1}+\left(\frac{\mathrm{1}}{\mathrm{6}^{\mathrm{n}} }\right)\right)^{\frac{\mathrm{1}}{\mathrm{n}}} \right)\:=\:\mathrm{3}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{6}^{\mathrm{n}} }\right)^{\frac{\mathrm{1}}{\mathrm{n}}} \\…
Question Number 164364 by Zaynal last updated on 16/Jan/22 $$\boldsymbol{{Lim}}_{\boldsymbol{{x}}\rightarrow\infty} \:\left(\boldsymbol{{e}}^{\boldsymbol{{tan}}\left(\boldsymbol{{x}}\right)} \right) \\ $$$$\left\{\boldsymbol{{Z}}.\boldsymbol{\mathrm{A}}\right\} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 98823 by john santu last updated on 16/Jun/20 Commented by bramlex last updated on 16/Jun/20 $${L}'{Hopital}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}+{x}\mathrm{cos}\:{x}}{\mathrm{3}{x}^{\mathrm{2}} }\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{cos}\:{x}+\mathrm{cos}\:{x}−{x}\mathrm{sin}\:{x}}{\mathrm{6}{x}} \\ $$$$\underset{{x}\rightarrow\mathrm{0}}…
Question Number 98788 by Ar Brandon last updated on 16/Jun/20 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\mathrm{n}}\left[\:\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{2}\right)…\left(\mathrm{n}+\mathrm{n}\right)_{} ^{} \right]^{\frac{\mathrm{1}}{\mathrm{n}}} \\ $$ Answered by Ar Brandon last updated on 16/Jun/20 Answered…
Question Number 98773 by john santu last updated on 16/Jun/20 $$\mathrm{if}\:\mathrm{x}\:\mathrm{is}\:\mathrm{a}\:\mathrm{selected}\:\mathrm{number}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{from}\:\mathrm{20}−\mathrm{99},\:\mathrm{then}\:\mathrm{what} \\ $$$$\mathrm{is}\:\mathrm{probalility}\:\mathrm{x}^{\mathrm{3}} −\mathrm{x}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{by} \\ $$$$\mathrm{12}?\: \\ $$ Answered by mr W last…
Question Number 98768 by bemath last updated on 16/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}+\mathrm{1}}\:\mathrm{sin}\:\mathrm{x}+\mathrm{ln}\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)−\mathrm{x}}{\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }−\mathrm{1}} \\ $$ Answered by john santu last updated on 16/Jun/20 Commented by…
Question Number 33168 by abdo imad last updated on 11/Apr/18 $${find}\:{lim}_{{n}\rightarrow\infty} \:\:\:\int_{{n}} ^{{n}+\mathrm{1}} \:\:\:\frac{\left({t}+{n}\right)^{\frac{\mathrm{1}}{\mathrm{3}}} }{\:\sqrt{{t}}}\:{dt}\:. \\ $$ Commented by abdo imad last updated on 13/Apr/18…
Question Number 98616 by bemath last updated on 15/Jun/20 Answered by bobhans last updated on 15/Jun/20 $$\underset{\mathrm{n}\rightarrow\infty\:} {\mathrm{lim}}\:\left(\frac{\sqrt{\mathrm{5}}}{\:\sqrt{\mathrm{9}+\mathrm{9}}}\right)^{\mathrm{n}} \:=\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\sqrt{\mathrm{5}}}{\:\sqrt{\mathrm{18}}}\right)^{\mathrm{n}} \\ $$$$=\:\sqrt{\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{5}}{\mathrm{18}}\right)^{\mathrm{n}} }\:=\:\mathrm{0}\:.\:\blacksquare \\…
Question Number 33073 by NECx last updated on 10/Apr/18 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{2}} {e}^{−{x}} \\ $$ Commented by abdo imad last updated on 10/Apr/18 $${for}\:{all}\:{plynome}\:{p}\left({x}\right)\:{not}\:{o}\:{wehave}\:{lim}_{{x}\rightarrow+\infty} {p}\left({x}\right){e}^{−\alpha{x}} =\mathrm{0}…