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Category: Limits

Lim-x-4x-2-8x-3-2x-4-

Question Number 82541 by zainal tanjung last updated on 22/Feb/20 $$\:\underset{\mathrm{x}\rightarrow\infty} {\mathrm{Lim}}\:\sqrt{\mathrm{4x}^{\mathrm{2}} −\mathrm{8x}+\mathrm{3}}\:−\mathrm{2x}−\mathrm{4} \\ $$ Commented by john santu last updated on 22/Feb/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\mathrm{4}{x}^{\mathrm{2}}…

Find-the-limit-x-0-lim-tan-x-x-1-x-2-

Question Number 82494 by niroj last updated on 21/Feb/20 $$\:\: \\ $$$$\:\:\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{limit}} \\ $$$$\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\overset{\boldsymbol{\mathrm{lim}}} {\:}}\:\left(\frac{\boldsymbol{\mathrm{tan}}\:\boldsymbol{\mathrm{x}}}{\boldsymbol{\mathrm{x}}}\right)^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{x}}^{\:\mathrm{2}} }} \\ $$ Commented by abdomathmax last updated on…

Lim-x-pi-2-sin-6x-3pi-2-sin-6x-3pi-sin-4x-2pi-5x-2-cos-5x-5pi-2-

Question Number 82448 by zainal tanjung last updated on 21/Feb/20 $$\underset{\mathrm{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{Lim}}\:\left\{\frac{\mathrm{sin}\:\left(\mathrm{6x}−\mathrm{3}\pi\right)^{\mathrm{2}} −\mathrm{sin}\:\left(\mathrm{6x}−\mathrm{3}\pi\right)\mathrm{sin}\:\left(\mathrm{4x}−\mathrm{2}\pi\right)}{\mathrm{5x}^{\mathrm{2}} \:\mathrm{cos}\:\left(\mathrm{5x}−\frac{\mathrm{5}\pi}{\mathrm{2}}\:\right)}\right. \\ $$ Commented by jagoll last updated on 21/Feb/20 $${let}\:{x}−\frac{\pi}{\mathrm{2}}\:=\:{u} \\…

Lim-1-ex-6x-x-0-

Question Number 82425 by zainal tanjung last updated on 21/Feb/20 $$\mathrm{Lim}\:\left(\frac{\mathrm{1}}{\mathrm{ex}}\right)^{\mathrm{6x}} =….. \\ $$$$\mathrm{x}\rightarrow\mathrm{0} \\ $$ Commented by abdomathmax last updated on 21/Feb/20 $${let}\:{f}\left({x}\right)=\left(\frac{\mathrm{1}}{{ex}}\right)^{\mathrm{6}{x}} \:\Rightarrow{f}\left({x}\right)={e}^{−\mathrm{6}{xln}\left({ex}\right)}…

lim-x-0-arctan-x-arcsin-x-sin-3-x-

Question Number 147738 by liberty last updated on 23/Jul/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{arctan}\:{x}−\mathrm{arcsin}\:{x}}{\mathrm{sin}\:^{\mathrm{3}} {x}}\:=? \\ $$ Answered by gsk2684 last updated on 23/Jul/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{tan}^{−\mathrm{1}} {x}−\mathrm{sin}^{−\mathrm{1}} {x}}{\mathrm{sin}\:^{\mathrm{3}}…

prove-that-lim-x-n-2-1-cos-1-n-1-cos-1-n-1-cos-1-n-1-2-

Question Number 82160 by M±th+et£s last updated on 18/Feb/20 $${prove}\:{that} \\ $$$$\underset{{x}\rightarrow\infty} {{lim}}\:{n}^{\mathrm{2}} \:\sqrt{\left(\mathrm{1}−{cos}\left(\frac{\mathrm{1}}{{n}}\right)\sqrt{\left(\mathrm{1}−{cos}\frac{\mathrm{1}}{{n}}\right)\sqrt{\left(\mathrm{1}−{cos}\frac{\mathrm{1}}{{n}}\right)…}}\right.}\:=\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by MJS last updated on 18/Feb/20 $${w}=\sqrt{\left(\mathrm{1}−\mathrm{cos}\:\frac{\mathrm{1}}{{n}}\right)\sqrt{\left(\mathrm{1}−\mathrm{cos}\:\frac{\mathrm{1}}{{n}}\right)\sqrt{…}}} \\…