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Category: Limits

Question-94730

Question Number 94730 by i jagooll last updated on 20/May/20 Answered by john santu last updated on 20/May/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\mathrm{e}^{\mathrm{ln}\left(\mathrm{x}\right)^{\mathrm{sin}\:\mathrm{x}} } =\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{e}^{\mathrm{sin}\:\mathrm{x}.\:\mathrm{ln}\left(\mathrm{x}\right)} \\…

lim-x-a-x-1-m-a-1-m-x-1-n-a-1-n-Don-t-use-L-hospital-rules-

Question Number 29180 by A1B1C1D1 last updated on 05/Feb/18 $$\underset{\mathrm{x}\:\rightarrow\:\mathrm{a}} {\mathrm{lim}}\:\left(\frac{\sqrt[{\mathrm{m}}]{\mathrm{x}}\:−\:\sqrt[{\mathrm{m}}]{\mathrm{a}}}{\:\sqrt[{\mathrm{n}}]{\mathrm{x}}\:−\:\sqrt[{\mathrm{n}}]{\mathrm{a}}}\right) \\ $$$$\left.\mathrm{Don}'\mathrm{t}\:\mathrm{use}\:\mathrm{L}'\mathrm{hospital}\:\mathrm{rules}\::-\right) \\ $$ Answered by Rasheed.Sindhi last updated on 05/Feb/18 $$\mathrm{Formula} \\ $$$$\:\:\:\:\:\:\:\:\:\:\underset{\mathrm{x}\rightarrow\mathrm{a}}…

Li-x-0-m-tan-1-x-tan-x-sin-1-x-sin-x-

Question Number 160244 by cortano last updated on 26/Nov/21 $$\:\:\:\:\:{L}\underset{{x}\rightarrow\mathrm{0}} {{i}m}\:\left(\frac{\mathrm{tan}^{−\mathrm{1}} \left({x}\right)−\mathrm{tan}\:\left({x}\right)}{\mathrm{sin}^{−\mathrm{1}} \left({x}\right)−\mathrm{sin}\:\left({x}\right)}\right)=? \\ $$ Answered by FongXD last updated on 26/Nov/21 $$\mathrm{L}=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\frac{\mathrm{tan}^{−\mathrm{1}} \mathrm{x}−\mathrm{tanx}}{\mathrm{x}^{\mathrm{3}}…

Question-160241

Question Number 160241 by mathlove last updated on 26/Nov/21 Commented by blackmamba last updated on 26/Nov/21 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{9}}]{\mathrm{7}{x}−\mathrm{6}}−\mathrm{1}}{{nx}^{\mathrm{3}} −{n}}\: \\ $$$$\:\:\:\:\:=\:\frac{\mathrm{1}}{{n}}\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{9}}]{\mathrm{7}{x}−\mathrm{6}}−\mathrm{1}}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)\left({x}−\mathrm{1}\right)} \\ $$$$\:\:\:\:\:=\:\frac{\mathrm{1}}{\mathrm{3}{n}}\:\underset{{x}\rightarrow\mathrm{1}}…

find-lim-x-1-3-2x-1-2-2-3x-1-x-3-

Question Number 29158 by abdo imad last updated on 04/Feb/18 $${find}\:{lim}_{{x}\rightarrow\mathrm{1}} \frac{\sqrt{\mathrm{3}+\sqrt{\mathrm{2}{x}−\mathrm{1}}}\:−\mathrm{2}}{\:\sqrt{\mathrm{2}+\sqrt{\mathrm{3}{x}+\mathrm{1}}}\:\:−\sqrt{{x}+\mathrm{3}}}\:\:. \\ $$ Commented by abdo imad last updated on 09/Feb/18 $${in}\:{this}\:{case}\:{its}\:{better}\:{to}\:{use}\:{hospital}\:{theorem}\:{let}\:{put} \\ $$$${u}\left({x}\right)=\sqrt{\mathrm{3}+\sqrt{\mathrm{2}{x}−\mathrm{1}}}\:−\mathrm{2}\:{and}\:{v}\left({x}\right)=\sqrt{\mathrm{2}+\sqrt{\mathrm{3}{x}+\mathrm{1}}}\:\:−\sqrt{{x}+\mathrm{3}}…