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Category: Limits

evaluate-lim-x-3-sinx-2x-1-sinx-x-2-1-

Question Number 174407 by infinityaction last updated on 31/Jul/22 $$\:{evaluate} \\ $$$$\:\:\:\underset{{x}\rightarrow−\infty} {\mathrm{lim}}\:\frac{\mathrm{3}^{\mathrm{sin}{x}\:} +\mathrm{2}{x}\:+\mathrm{1}}{\mathrm{sin}{x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\:} \\ $$ Answered by CElcedricjunior last updated on 31/Jul/22 $$\underset{{x}\rightarrow−\infty}…

Question-174331

Question Number 174331 by cortano1 last updated on 30/Jul/22 Commented by kaivan.ahmadi last updated on 30/Jul/22 $$\overset{{hop}} {\sim}\:{li}\underset{{x}\rightarrow\infty} {{m}}\:\frac{\frac{\mathrm{3}{e}^{\mathrm{3}{x}} }{\mathrm{2}+{e}^{\mathrm{3}{x}} }}{\frac{\mathrm{2}{e}^{\mathrm{2}{x}} }{\mathrm{3}+{e}^{\mathrm{2}{x}} }}={li}\underset{{x}\rightarrow\infty} {{m}}\frac{\mathrm{3}{e}^{\mathrm{3}{x}} \left(\mathrm{3}+{e}^{\mathrm{2}{x}}…

Question-174327

Question Number 174327 by aminee last updated on 30/Jul/22 Answered by Mathspace last updated on 31/Jul/22 $${we}\:{have}\:{sin}\left({a}+{b}\right)={sina}.{cosb}+{cosasinb} \\ $$$${sin}\left({a}−{b}\right)={sinacosb}−{cosasinb}\:\Rightarrow \\ $$$$\mathrm{2}{sina}.{cosb}={sin}\left({a}+{b}\right)+{sin}\left({a}−{b}\right)\:\Rightarrow \\ $$$${sina}.{cosb}=\frac{\mathrm{1}}{\mathrm{2}}\left\{{sin}\left({a}+{b}\right)+{sin}\left({a}−{b}\right)\right\} \\ $$$$\Rightarrow\sum_{{n}=\mathrm{1}}…

BeMath-lim-x-0-1-cos-xcos-2xcos-3xcos-4x-cos-nx-x-2-

Question Number 108757 by bemath last updated on 19/Aug/20 $$\:\:\frac{\vdots\mathcal{B}{e}\mathcal{M}{ath}\vdots}{\triangleright\heartsuit\triangleleft} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{cos}\:{x}\mathrm{cos}\:\mathrm{2}{x}\mathrm{cos}\:\mathrm{3}{x}\mathrm{cos}\:\mathrm{4}{x}…\mathrm{cos}\:{nx}}}{{x}^{\mathrm{2}} }\:=? \\ $$ Answered by bemath last updated on 19/Aug/20 Terms of…

Question-174276

Question Number 174276 by cortano1 last updated on 28/Jul/22 Answered by blackmamba last updated on 28/Jul/22 $$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt[{\mathrm{2022}}]{\mathrm{cos}\:\left(\mathrm{2021}{x}\right)}}{{x}^{\mathrm{2}} }\:= \\ $$$$\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt[{\mathrm{2022}}]{\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}} \left(\frac{\mathrm{2021}{x}}{\mathrm{2}}\right)}}{{x}^{\mathrm{2}} } \\…

lim-x-x-4-x-3-x-

Question Number 174258 by blackmamba last updated on 28/Jul/22 $$\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\sqrt{\sqrt{{x}^{\mathrm{4}} −{x}^{\mathrm{3}} }}\:−\:{x}\:=? \\ $$ Answered by cortano1 last updated on 28/Jul/22 $$\:\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt{{x}^{\mathrm{4}} −{x}^{\mathrm{3}}…

BeMath-1-lim-b-a-b-a-a-b-a-a-b-a-2a-a-2-lim-x-0-3e-2x-e-x-4-x-

Question Number 108623 by bemath last updated on 18/Aug/20 $$\:\:\frac{\supset\mathcal{B}{e}\mathcal{M}{ath}\supset}{\bigstar} \\ $$$$\:\left(\mathrm{1}\right)\underset{{b}\rightarrow{a}} {\mathrm{lim}}\:\frac{{b}\sqrt{{a}}−{a}\sqrt{{b}}}{{a}\sqrt{{a}}+{b}\sqrt{{a}}−\mathrm{2}{a}\sqrt{{a}}} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3}{e}^{\mathrm{2}{x}} +{e}^{{x}} −\mathrm{4}}{{x}} \\ $$ Answered by ajfour last updated…

lim-x-0-1-sin-pi-2-cos-x-2x-5x-2-

Question Number 174152 by cortano1 last updated on 26/Jul/22 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}\mathrm{cos}\:{x}+\mathrm{2}{x}\right)}{\mathrm{5}{x}^{\mathrm{2}} }\:=? \\ $$ Answered by CElcedricjunior last updated on 26/Jul/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}−{sin}\left(\frac{\boldsymbol{\pi}}{\mathrm{2}}{cosx}+\mathrm{2}{x}\right)}{\mathrm{5}\boldsymbol{{x}}^{\mathrm{2}} }=\frac{\mathrm{0}}{\mathrm{0}}=\boldsymbol{{F}\mathrm{I}} \\…