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Category: Limits

lim-x-x-2-sin-x-x-x-2-1-

Question Number 84873 by john santu last updated on 17/Mar/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{x}^{\mathrm{2}} \mathrm{sin}\:\left(\frac{\mathrm{x}!}{\mathrm{x}}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}} \\ $$ Commented by john santu last updated on 17/Mar/20 $$\mathrm{yes}.\:\mathrm{i}\:\mathrm{agree}\:\mathrm{sir}…

lim-x-pi-2-cos-2-x-2-2-1-cos-x-x-pi-3-

Question Number 19271 by Joel577 last updated on 08/Aug/17 $$\underset{{x}\rightarrow\pi} {\mathrm{lim}}\:\left(\mathrm{2}\:−\:\mathrm{cos}^{\mathrm{2}} \:{x}\right)^{\frac{\mathrm{2}\sqrt{\mathrm{2}\left(\mathrm{1}\:+\:\mathrm{cos}\:{x}\right)}}{\left({x}\:−\:\pi\right)^{\mathrm{3}} }} \\ $$ Answered by ajfour last updated on 09/Aug/17 $$=\underset{{x}\rightarrow\pi} {\mathrm{lim}}\left\{\left[\mathrm{1}+\mathrm{sin}\:^{\mathrm{2}} \left(\pi−\mathrm{x}\right)\right]^{\frac{\mathrm{1}}{\mathrm{sin}\:^{\mathrm{2}}…

lim-x-x-x-1-9x-2-x-3-

Question Number 84600 by john santu last updated on 14/Mar/20 $$\underset{{x}\rightarrow\infty\:} {\mathrm{lim}}\:{x}\sqrt{\frac{{x}−\mathrm{1}}{\mathrm{9}{x}+\mathrm{2}}}\:−\:\frac{{x}}{\mathrm{3}} \\ $$ Commented by jagoll last updated on 14/Mar/20 $$\mathrm{nice}\:\mathrm{mister} \\ $$ Commented…

without-L-hopital-lim-x-1-2-2x-3-3x-2-a-bx-4x-2-1-3-4-find-a-b-

Question Number 84568 by jagoll last updated on 14/Mar/20 $$\mathrm{without}\:\mathrm{L}'\mathrm{hopital} \\ $$$$\underset{{x}\rightarrow−\frac{\mathrm{1}}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{2x}^{\mathrm{3}} +\mathrm{3x}^{\mathrm{2}} −\sqrt{\mathrm{a}+\mathrm{bx}}}{\mathrm{4x}^{\mathrm{2}} −\mathrm{1}}\:=\:−\frac{\mathrm{3}}{\mathrm{4}} \\ $$$$\mathrm{find}\:\mathrm{a}+\mathrm{b} \\ $$ Commented by john santu last…

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

Question Number 84492 by john santu last updated on 13/Mar/20 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left({x}−\frac{\pi}{\mathrm{3}}\right)}{\mathrm{1}−\mathrm{2cos}\:\left({x}\right)}\:=\: \\ $$ Commented by john santu last updated on 13/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left({x}\right)}{\mathrm{1}−\mathrm{2cos}\:\left({x}+\frac{\pi}{\mathrm{3}}\right)}\:= \\…

lim-x-0-sin-2-x-sin-2-x-x-

Question Number 84460 by jagoll last updated on 13/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{2}+\mathrm{x}\right)−\mathrm{sin}\:\left(\mathrm{2}−\mathrm{x}\right)}{\mathrm{x}} \\ $$ Commented by jagoll last updated on 13/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\left(\mathrm{2}+\mathrm{x}\right)+\mathrm{cos}\:\left(\mathrm{2}−\mathrm{x}\right)}{\mathrm{1}} \\ $$$$=\:\mathrm{2cos}\:\mathrm{2} \\…

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

Question Number 84377 by john santu last updated on 12/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{1}+\mathrm{tan}\:\mathrm{x}}−\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\mathrm{2}} \mathrm{sin}\:\mathrm{x}} \\ $$ Answered by john santu last updated on 12/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{tan}\:\mathrm{x}}+\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{x}}}\:×\:\underset{{x}\rightarrow\mathrm{0}}…