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Category: Limits

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}}…

lim-x-pi-tan-x-1-cos-x-

Question Number 160609 by cortano last updated on 03/Dec/21 $$\:\:\:\:\:\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\left(\frac{\mathrm{tan}\:\mathrm{x}}{\mathrm{1}+\mathrm{cos}\:\mathrm{x}}\right)=? \\ $$ Answered by Ar Brandon last updated on 03/Dec/21 $$\mathscr{L}=\underset{{x}\rightarrow\pi} {\mathrm{lim}}\left(\frac{\mathrm{tan}{x}}{\mathrm{1}+\mathrm{cos}{x}}\right),\:{u}={x}−\pi \\ $$$$\:\:\:\:\:=\underset{{u}\rightarrow\mathrm{0}}…

S-n-12-4-2-3-2-4-2-3-2-12-2-4-2-3-2-4-3-3-3-12-3-4-2-3-2-4-4-3-4-12-n-4-2-3-2-4-n-1-3-n-1-lim-n-S-n-

Question Number 160604 by cortano last updated on 03/Dec/21 $$\:\:\mathrm{S}_{\mathrm{n}} =\:\frac{\mathrm{12}}{\left(\mathrm{4}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} \right)\left(\mathrm{4}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} \right)}+\frac{\mathrm{12}^{\mathrm{2}} }{\left(\mathrm{4}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} \right)\left(\mathrm{4}^{\mathrm{3}} −\mathrm{3}^{\mathrm{3}} \right)}+\frac{\mathrm{12}^{\mathrm{3}} }{\left(\mathrm{4}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} \right)\left(\mathrm{4}^{\mathrm{4}} −\mathrm{3}^{\mathrm{4}} \right)}+…+\frac{\mathrm{12}^{\mathrm{n}}…

find-lim-n-n-2-2n-

Question Number 29511 by abdo imad last updated on 09/Feb/18 $${find}\:{lim}_{{n}\rightarrow+\infty} \:\:\:\:\:\:\frac{\left({n}!\right)^{\mathrm{2}} }{\left(\mathrm{2}{n}\right)!}\:. \\ $$ Commented by prof Abdo imad last updated on 12/Feb/18 $${let}\:{use}\:{stirling}\:{formula}\:{we}\:{have}…