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Category: Limits

find-lim-x-0-tanx-x-1-3-x-3-x-5-

Question Number 29845 by abdo imad last updated on 12/Feb/18 $${find}\:\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\:\:\frac{{tanx}\:−{x}−\frac{\mathrm{1}}{\mathrm{3}}{x}^{\mathrm{3}} }{{x}^{\mathrm{5}} }\:\:. \\ $$ Commented by Cheyboy last updated on 13/Feb/18 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sec}^{\mathrm{2}}…

lim-x-0-tan-x-2-tan-2-x-tan-2-2-3x-tan-x-

Question Number 160912 by cortano last updated on 09/Dec/21 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{tan}\:\left(\mathrm{x}+\mathrm{2}\right)\mathrm{tan}\:\left(\mathrm{2}−\mathrm{x}\right)−\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{2}\right)}{\mathrm{3x}\:\mathrm{tan}\:\mathrm{x}}\:=? \\ $$ Answered by blackmamba last updated on 09/Dec/21 $$\:\begin{cases}{\mathrm{tan}\:\left({x}+\mathrm{2}\right)=\frac{\mathrm{tan}\:\mathrm{2}+\mathrm{tan}\:{x}}{\mathrm{1}−\mathrm{tan}\:\mathrm{2}\:\mathrm{tan}\:{x}}}\\{\mathrm{tan}\:\left(\mathrm{2}−{x}\right)=\frac{\mathrm{tan}\:\mathrm{2}−\mathrm{tan}\:{x}}{\mathrm{1}+\mathrm{tan}\:\mathrm{2}\:\mathrm{tan}\:{x}}}\\{\mathrm{tan}\:\left({x}+\mathrm{2}\right)\mathrm{tan}\:\left(\mathrm{2}−{x}\right)=\frac{\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{2}\right)−\mathrm{tan}\:^{\mathrm{2}} \left({x}\right)}{\mathrm{1}−\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{2}\right)\mathrm{tan}\:^{\mathrm{2}}…

lim-n-k-1-n-n-1-k-n-2-k-2-sin-1-n-

Question Number 160885 by qaz last updated on 08/Dec/21 $$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}+\frac{\mathrm{1}}{\mathrm{k}}}{\:\sqrt{\mathrm{n}^{\mathrm{2}} +\mathrm{k}^{\mathrm{2}} }}\centerdot\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{n}}=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

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…