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Category: Limits

Question-106072

Question Number 106072 by bemath last updated on 02/Aug/20 Answered by bobhans last updated on 02/Aug/20 $$\underset{{x}\rightarrow\pi/\mathrm{2}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{2sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{3sin}\:\mathrm{x}+\mathrm{4}}}{\mathrm{cot}\:^{\mathrm{2}} \mathrm{x}}\:= \\ $$$$\mathrm{set}\:\mathrm{x}\:=\:\frac{\pi}{\mathrm{2}}+\mathrm{h}\:\Rightarrow\underset{\mathrm{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3}}{\mathrm{cot}\:^{\mathrm{2}} \left(\mathrm{h}+\frac{\pi}{\mathrm{2}}\right)}\:= \\…

lim-x-0-cos-x-1-x-please-i-need-your-help-

Question Number 105868 by pticantor last updated on 01/Aug/20 $$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}cos}}\left(\frac{\sqrt{\boldsymbol{{x}}}−\mathrm{1}}{\boldsymbol{{x}}}\right)=????? \\ $$$${pl}\boldsymbol{{ease}}\:\boldsymbol{{i}}\:\boldsymbol{{need}}\:\boldsymbol{{your}}\:\boldsymbol{{help}} \\ $$ Commented by…

lim-x-0-x-2-sin3x-2x-sinx-

Question Number 171341 by mathlove last updated on 13/Jun/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} +{sin}\mathrm{3}{x}}{\mathrm{2}{x}−{sinx}}=? \\ $$ Commented by infinityaction last updated on 13/Jun/22 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\cancel{{x}}\left({x}+\frac{\mathrm{3sin}\:\mathrm{3}{x}}{\mathrm{3}{x}}\right)}{\cancel{{x}}\left(\mathrm{2}−\frac{\mathrm{sin}\:{x}}{{x}}\right)} \\ $$$$\:\:\:\:\frac{\mathrm{0}+\mathrm{3}}{\mathrm{2}−\mathrm{1}}\:=\:\mathrm{3}…