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Question Number 188826 by mathlove last updated on 08/Mar/23 $${prove}\:{that} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\sqrt[{{n}\left({n}+\mathrm{1}\right)}]{\mathrm{1}!\:\mathrm{2}!\:\mathrm{3}!\centerdot\centerdot\centerdot\centerdot\centerdot{n}!}}{\:\sqrt{{n}}}={e}^{\frac{−\mathrm{3}}{\mathrm{4}}} \\ $$ Commented by Frix last updated on 07/Mar/23 $$\mathrm{There}\:\mathrm{is}\:\mathrm{no}\:{x}\:\mathrm{and}\:\mathrm{why}\:\rightarrow\mathrm{0}? \\ $$…
Question Number 188819 by mnjuly1970 last updated on 07/Mar/23 $$ \\ $$$$\:\:\:\:\:\:\:\mathrm{calculate}\: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{lim}_{\:{x}\rightarrow\:\mathrm{0}^{\:+} } \left(\:\sqrt{\:\mathrm{cos}\:\left(\:\sqrt{{x}}\:\right)}\:\right)^{\:\mathrm{cot}\left(\:{x}\:\right)} \:=\:?\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$$$ \\ $$…
Question Number 188798 by mathlove last updated on 07/Mar/23 Answered by ARUNG_Brandon_MBU last updated on 07/Mar/23 $$\mathscr{L}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}^{{x}} \mathrm{3}^{{x}} \mathrm{4}^{{x}} \mathrm{5}^{{x}} …{n}^{{x}} −\mathrm{1}}{{x}} \\ $$$$\:\:\:\:\:=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 188771 by mnjuly1970 last updated on 06/Mar/23 Commented by mahdipoor last updated on 06/Mar/23 $${lim}\:\left({x}\rightarrow\mathrm{0}^{+} \right)\:\:\:\:\:\:\sqrt{{cos}\left(\sqrt{{cos}\left({x}\right)}\right)}=\sqrt{{cos}\left(\mathrm{1}\right)}={a} \\ $$$$\Rightarrow\mathrm{0}<{a}<\frac{\mathrm{1}}{\mathrm{2}}\overset{{b}>\mathrm{0}} {\Rightarrow}\mathrm{0}^{{b}} <{a}^{{b}} <\mathrm{1}^{{b}} \Rightarrow\mathrm{0}<{a}^{{b}} <\frac{\mathrm{1}}{\mathrm{2}^{{b}}…
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Question Number 188699 by cortano12 last updated on 05/Mar/23 $$\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}−\mathrm{sec}\:\mathrm{x}\:\mathrm{tan}\:\mathrm{x}\:\right)=? \\ $$ Answered by mehdee42 last updated on 05/Mar/23 $${li}\underset{{x}\rightarrow\infty} {{m}}\left(\frac{\mathrm{1}−{sinx}}{{cos}^{\mathrm{2}} {x}}\right)={li}\underset{{x}\rightarrow\infty} {{m}}\left(\frac{\mathrm{1}}{\mathrm{1}+{sinx}}\right)={A}…
Question Number 188575 by mathlove last updated on 03/Mar/23 Answered by universe last updated on 03/Mar/23 $$\sqrt{{e}} \\ $$ Answered by floor(10²Eta[1]) last updated on…
Question Number 188521 by Rupesh123 last updated on 02/Mar/23 Commented by SEKRET last updated on 02/Mar/23 $$\:\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Commented by Rupesh123 last updated on…
Question Number 57442 by rahul 19 last updated on 04/Apr/19 $$\left.\mathrm{1}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}}{{e}^{\frac{\mathrm{1}}{{x}}} +\mathrm{1}}\:=\:? \\ $$$$\left.\mathrm{2}\right)\:{For}\:{x}\epsilon{R},\:{f}\left({x}\right)=\mid{ln}\mathrm{2}−\mathrm{sin}\:{x}\mid\:{and}\: \\ $$$${g}\left({x}\right)={f}\left({f}\left({x}\right)\right),\:{then}\:{prove}\:{that}\: \\ $$$${g}'\left(\mathrm{0}\right)=\mathrm{cos}\:\left({ln}\mathrm{2}\right). \\ $$ Commented by rahul 19…