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Category: Limits

a-n-is-root-of-equation-x-n-x-1-a-n-0-1-Find-lim-n-n-na-n-lnn-ln-lnn-

Question Number 160886 by qaz last updated on 08/Dec/21 $$\mathrm{a}_{\mathrm{n}} \:\mathrm{is}\:\mathrm{root}\:\mathrm{of}\:\mathrm{equation}\:\mathrm{x}^{\mathrm{n}} +\mathrm{x}=\mathrm{1},\mathrm{a}_{\mathrm{n}} \in\left(\mathrm{0},\mathrm{1}\right). \\ $$$$\mathrm{Find}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{n}−\mathrm{na}_{\mathrm{n}} −\mathrm{lnn}}{\mathrm{ln}\left(\mathrm{lnn}\right)}=? \\ $$ Terms of Service Privacy Policy Contact:…

lim-n-5-n-7-n-1-n-

Question Number 160875 by cortano last updated on 08/Dec/21 $$\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\sqrt[{\mathrm{n}}]{\mathrm{5}^{\mathrm{n}} +\mathrm{7}^{\mathrm{n}} }\:=? \\ $$ Answered by MJS_new last updated on 08/Dec/21 $$\left(\mathrm{5}^{{n}} +\mathrm{7}^{{n}} \right)^{\mathrm{1}/{n}}…

lim-n-0-1-1-sin-pit-2-n-dt-1-n-

Question Number 160825 by qaz last updated on 07/Dec/21 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\left[\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}+\mathrm{sin}\:\frac{\pi\mathrm{t}}{\mathrm{2}}\right)^{\mathrm{n}} \mathrm{dt}\right]^{\frac{\mathrm{1}}{\mathrm{n}}} =? \\ $$ Answered by mnjuly1970 last updated on 07/Dec/21 $${answer}\::\:\:\Omega\::=\:{sup}_{\:\left[\:\mathrm{0}\:,\mathrm{1}\:\right]}…

lim-n-n-cos-x-1-x-2-n-dx-

Question Number 160796 by qaz last updated on 06/Dec/21 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{n}}\int_{−\infty} ^{+\infty} \frac{\mathrm{cos}\:\mathrm{x}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{n}} }\mathrm{dx}=? \\ $$ Answered by mathmax by abdo last updated on…

lim-x-0-2-cos-x-2-x-2-

Question Number 160793 by cortano last updated on 06/Dec/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}^{\mathrm{cos}\:\mathrm{x}} \:−\:\mathrm{2}}{\mathrm{x}^{\mathrm{2}} }\:=? \\ $$ Answered by qaz last updated on 06/Dec/21 $$\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}^{\mathrm{cos}\:\mathrm{x}} −\mathrm{2}}{\mathrm{x}^{\mathrm{2}}…

lim-x-0-7-x-1-2-x-1-

Question Number 95230 by i jagooll last updated on 24/May/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{7}^{\sqrt{\mathrm{x}}} \:−\mathrm{1}}{\mathrm{2}^{\sqrt{\mathrm{x}}} \:−\mathrm{1}}\:=\:? \\ $$ Answered by bobhans last updated on 24/May/20 $$\underset{{x}\rightarrow\mathrm{0}^{+}…

find-lim-x-0-2-1-a-x-1-x-

Question Number 29689 by mrW2 last updated on 11/Feb/18 $${find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{2}}{\mathrm{1}+{a}^{{x}} }\right)^{\frac{\mathrm{1}}{{x}}} =? \\ $$ Commented by abdo imad last updated on 13/Feb/18 $${let}\:{put}\:{A}\left({x}\right)=\left(\frac{\mathrm{2}}{\mathrm{1}+{a}^{{x}} }\right)^{\frac{\mathrm{1}}{{x}}}…

lim-x-x-2-e-2x-

Question Number 95133 by john santu last updated on 23/May/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{x}^{\mathrm{2}} .\mathrm{e}^{\:−\mathrm{2x}} \right)\:=\:? \\ $$ Answered by bobhans last updated on 23/May/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{2}}…