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Category: Limits

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

Question Number 159754 by cortano last updated on 20/Nov/21 $$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\sqrt{\mathrm{tan}\:{x}}\:+\:\sqrt{\mathrm{sin}\:{x}}\:−\mathrm{2}\sqrt{{x}}}{\:\sqrt{\mathrm{sin}\:{x}}\:−\:\sqrt{\mathrm{tan}\:{x}}\:}\:=\:? \\ $$ Answered by bobhans last updated on 21/Nov/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\sqrt{\mathrm{tan}\:\mathrm{x}}\:+\sqrt{\mathrm{sin}\:\mathrm{x}}−\mathrm{2}\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{sin}\:\mathrm{x}}−\sqrt{\mathrm{tan}\:\mathrm{x}}}\: \\…

lim-x-0-1-tan-1-x-sin-x-1-x-3-

Question Number 159727 by blackmamba last updated on 20/Nov/21 $$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\sqrt[{{x}^{\mathrm{3}} }]{\mathrm{1}+\mathrm{tan}\:\left(\mathrm{1}−\left(\frac{{x}}{\mathrm{sin}\:{x}}\right)\right)}\:?\: \\ $$ Answered by FongXD last updated on 20/Nov/21 $$\mathrm{L}=\underset{\mathrm{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\left[\mathrm{1}+\mathrm{tan}\left(\mathrm{1}−\frac{\mathrm{x}}{\mathrm{sinx}}\right)\right]^{\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{3}} }}…

L-lim-x-pi-3-3-4sin-2-x-sin-2x-sin-x-Q-lim-x-0-1-x-2-2-cos-2-x-cos-x-3-

Question Number 159720 by tounghoungko last updated on 20/Nov/21 $$\:\:\:\:\:\:\:\:{L}\:=\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {\mathrm{lim}}\:\frac{\mathrm{3}−\mathrm{4sin}\:^{\mathrm{2}} {x}}{\mathrm{sin}\:\mathrm{2}{x}−\mathrm{sin}\:{x}}\:? \\ $$$$\:\:\:\:\:\:{Q}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:\left(\frac{\mathrm{2}}{\mathrm{cos}\:^{\mathrm{2}} {x}}\:+\mathrm{cos}\:{x}−\mathrm{3}\right)\right]\:?\: \\ $$ Commented by cortano last updated on…