Question Number 132007 by abdullahquwatan last updated on 10/Feb/21 Answered by bramlexs22 last updated on 10/Feb/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{2x}+\mathrm{sin}\:\mathrm{3x}\left(\mathrm{cos}\:\mathrm{x}−\mathrm{cos}\:\mathrm{2x}\right)−\mathrm{cos}\:\mathrm{x}}{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{cos}\:\mathrm{2x}−\mathrm{1}} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{cos}\:\mathrm{2x}−\mathrm{cos}\:\mathrm{x}\right)\left(\mathrm{1}−\mathrm{sin}\:\mathrm{3x}\right)}{\mathrm{cos}\:\mathrm{2x}−\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}} \\ $$$$=\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 66444 by ~ À ® @ 237 ~ last updated on 15/Aug/19 $$\:{calculate}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\left({x}!\right)^{\frac{\mathrm{1}}{{x}}} \:\:\:\:\:\:\:{if}\:\:\:\:\:{x}!=\Pi\left({x}\right)=\int_{\mathrm{0}} ^{\infty} {t}^{{x}} \:{e}^{−{t}} {dt} \\ $$ Commented by…
Question Number 66434 by iklima_0412 last updated on 15/Aug/19 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{cos}^{\mathrm{2}} \mathrm{x}−\mathrm{x}}{\mathrm{1}−\mathrm{2x}} \\ $$ Commented by mathmax by abdo last updated on 15/Aug/19 $${let}\:{f}\left({x}\right)=\frac{{cos}^{\mathrm{2}} {x}−{x}}{\mathrm{1}−\mathrm{2}{x}}\:\Rightarrow\:{for}\:{x}\:\neq\mathrm{0}\:\:{we}\:{have}\:{f}\left({x}\right)=\frac{{x}−{cos}^{\mathrm{2}}…
Question Number 131962 by EDWIN88 last updated on 10/Feb/21 $$\:\underset{{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{ln}\:\mathrm{x}}\:−\:\frac{\mathrm{1}}{\mathrm{x}−\mathrm{1}}\right)=? \\ $$ Answered by liberty last updated on 10/Feb/21 $$\:\mathrm{let}\:\mathrm{u}=\mathrm{ln}\:\mathrm{x}\:\Rightarrow\mathrm{x}=\mathrm{e}^{\mathrm{u}} \\ $$$$\:\underset{\mathrm{u}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{u}}−\frac{\mathrm{1}}{\mathrm{e}^{\mathrm{u}}…
Question Number 66406 by ~ À ® @ 237 ~ last updated on 14/Aug/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 131938 by Raxreedoroid last updated on 09/Feb/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{\:\sqrt{{n}!}}=? \\ $$ Answered by Faetma last updated on 09/Feb/21 $$\left.\begin{matrix}{\underset{{n}\rightarrow+\infty} {\mathrm{lim}}\:{n}!=+\infty}\\{\underset{\mathrm{N}\rightarrow+\infty} {\mathrm{lim}}\:\sqrt{\mathrm{N}}=+\infty}\\{\underset{\mathrm{N}'\rightarrow+\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{N}'}=\mathrm{0}^{+} }\end{matrix}\right\}\underset{{n}\rightarrow+\infty}…
Question Number 131882 by Eric002 last updated on 09/Feb/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}}{{x}+\sqrt[{\mathrm{4}}]{{x}+\mathrm{1}}−\mathrm{1}} \\ $$ Answered by liberty last updated on 09/Feb/21 $$\:\mathrm{L}'\mathrm{H}\ddot {\mathrm{o}pital}\:\mathrm{L}=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\:\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}\:\sqrt[{\mathrm{4}}]{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{3}} }}}\:\right]=\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{4}}}=\:\frac{\mathrm{4}}{\mathrm{5}} \\…
Question Number 131836 by liberty last updated on 09/Feb/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}\left(\mathrm{2}+\mathrm{cos}\:\mathrm{x}\right)−\mathrm{3sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{5}} } \\ $$ Commented by EDWIN88 last updated on 10/Feb/21 $$\mathrm{another}\:\mathrm{way}\:\mathrm{L}'\mathrm{H}\hat {\mathrm{o}pital} \\ $$$$\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 131825 by liberty last updated on 09/Feb/21 $$\:\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{2n}−\mathrm{1}}{\mathrm{2}^{\mathrm{n}} }\:? \\ $$ Answered by mr W last updated on 09/Feb/21 $${method}\:\mathrm{1} \\…
Question Number 131789 by bemath last updated on 08/Feb/21 $$\mathrm{Let}\:\varphi\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{4}} +\mathrm{3}\left(\mathrm{a}^{\mathrm{2}} −\sqrt{\mathrm{a}^{\mathrm{4}} +\mathrm{x}^{\mathrm{4}} }\:\right)}{\mathrm{x}^{\mathrm{8}} }\:;\:\mathrm{a}>\mathrm{0} \\ $$$$\mathrm{If}\:\varphi\:\mathrm{is}\:\mathrm{finite}\:\mathrm{then}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{a}=\frac{\mathrm{3}}{\mathrm{2}}\:\:\:\:\left(\mathrm{b}\right)\:\mathrm{a}=\sqrt{\frac{\mathrm{3}}{\mathrm{2}}}\:\:\:\:\:\:\left(\mathrm{c}\right)\:\varphi=\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\:\left(\mathrm{d}\right)\:\varphi=\frac{\mathrm{1}}{\mathrm{9}} \\ $$ Answered by Dwaipayan…