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Category: Limits

advanced-mathematics-prove-that-lim-x-1-x-1-x-1-Euler-mascheroni-constant-m-n-huly-1970-

Question Number 116005 by mnjuly1970 last updated on 30/Sep/20 $$\:\:\:\:\:\:\:\:\:…\:{advanced}\:\:{mathematics}… \\ $$$$ \\ $$$$\:\:\:\:\:{prove}\:\:{that}::: \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{lim}_{{x}\rightarrow\mathrm{1}^{+} } \left(\:\zeta\left(\:{x}\:\right)\:−\frac{\mathrm{1}}{{x}\:−\:\mathrm{1}}\right)\:\overset{???} {=}\gamma\:\:\: \\ $$$$\:\:\gamma::\:\mathscr{E}{uler}\:−\:{mascheroni}\:{constant}. \\ $$$$…

lim-x-0-1-cos-x-cos-2x-cos-3x-1-3-cos-4x-1-4-x-2-

Question Number 115999 by bemath last updated on 30/Sep/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:{x}\:\sqrt{\mathrm{cos}\:\mathrm{2}{x}}\:\sqrt[{\mathrm{3}\:}]{\mathrm{cos}\:\mathrm{3}{x}}\:\sqrt[{\mathrm{4}\:}]{\mathrm{cos}\:\mathrm{4}{x}}}{{x}^{\mathrm{2}} } \\ $$ Answered by bobhans last updated on 30/Sep/20 $${short}\:{cut}\:'{mr}\:{john}\:{santu}\:' \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:{x}\:\sqrt{\mathrm{cos}\:\mathrm{2}{x}}\:\sqrt[{\mathrm{3}\:}]{\mathrm{cos}\:\mathrm{3}{x}}\:\sqrt[{\mathrm{4}\:}]{\mathrm{cos}\:\mathrm{4}{x}}}{{x}^{\mathrm{2}}…

Question-181462

Question Number 181462 by mathlove last updated on 25/Nov/22 Commented by Frix last updated on 26/Nov/22 $$\mathrm{I}\:\mathrm{think}\:\mathrm{it}'\mathrm{s}\:\frac{\mathrm{1}}{\mathrm{2e}}\:\mathrm{but}\:\mathrm{I}'\mathrm{m}\:\mathrm{not}\:\mathrm{100\%}\:\mathrm{sure} \\ $$$$\mathrm{Can}\:\mathrm{someone}\:\mathrm{confirm}\:\mathrm{this}? \\ $$ Answered by SEKRET last…

lim-x-0-1-cos-2x-1-3-2-1-3-x-2-sin-3x-

Question Number 115889 by bemath last updated on 29/Sep/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}\:}]{\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}}\:−\sqrt[{\mathrm{3}\:}]{\mathrm{2}}}{{x}^{\mathrm{2}} .\mathrm{sin}\:\mathrm{3}{x}} \\ $$ Answered by bemath last updated on 29/Sep/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{3}\:}]{\mathrm{1}+\left(\mathrm{1}−\frac{\mathrm{4}{x}^{\mathrm{2}} }{\mathrm{2}}\right)}−\sqrt[{\mathrm{3}\:}]{\mathrm{2}}}{{x}^{\mathrm{2}} .\mathrm{sin}\:\mathrm{3}{x}}\:=…

lim-x-0-cos-x-1-x-2-lim-x-e-3x-5x-1-x-lim-x-0-e-2x-2e-x-1-cos-3x-2cos-2x-cos-x-lim-x-0-1-x-2-cot-2-x-

Question Number 115780 by bemath last updated on 28/Sep/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{cos}\:{x}\right)^{\frac{\mathrm{1}}{{x}^{\mathrm{2}} }} \:=\:? \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left({e}^{\mathrm{3}{x}} −\mathrm{5}{x}\right)^{\frac{\mathrm{1}}{{x}}} \:=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{e}^{\mathrm{2}{x}} −\mathrm{2}{e}^{{x}} +\mathrm{1}}{\mathrm{cos}\:\mathrm{3}{x}−\mathrm{2cos}\:\mathrm{2}{x}+\mathrm{cos}\:{x}}=? \\ $$$$\underset{{x}\rightarrow\mathrm{0}}…

lim-x-0-sin-x-tan-1-x-x-2-ln-1-x-

Question Number 115777 by bemath last updated on 28/Sep/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}−\mathrm{tan}^{−\mathrm{1}} {x}}{{x}^{\mathrm{2}} \:\mathrm{ln}\:\left(\mathrm{1}+{x}\right)} \\ $$ Answered by bobhans last updated on 28/Sep/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left({x}−\frac{{x}^{\mathrm{3}} }{\mathrm{6}}+{Px}^{\mathrm{5}}…