Question Number 100134 by bemath last updated on 25/Jun/20 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{2}}} {\mathrm{lim}}\:\frac{\mathrm{4sin}\:\mathrm{x}−\sqrt{\mathrm{6}\sqrt{\mathrm{sin}\:\mathrm{x}}+\mathrm{10}}}{\frac{\pi}{\mathrm{2}}−\mathrm{x}}\:? \\ $$ Commented by bobhans last updated on 25/Jun/20 $$\mathrm{set}\:\frac{\pi}{\mathrm{2}}−\mathrm{x}\:=\:\mathrm{t}\:,\:\mathrm{x}\:=\frac{\pi}{\mathrm{2}}−\mathrm{t}\: \\ $$$$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{4cos}\:\mathrm{t}−\sqrt{\mathrm{6}\sqrt{\mathrm{cos}\:\mathrm{t}}+\mathrm{10}}}{\mathrm{t}}\:= \\…
Question Number 34554 by rahul 19 last updated on 07/May/18 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{{a}−\mathrm{1}+{b}^{\frac{\mathrm{1}}{{x}}} }{{a}}\right)^{{x}} =\:? \\ $$$$\left({a},{b}>\mathrm{0}\right) \\ $$ Commented by math khazana by abdo last…
Question Number 34540 by rahul 19 last updated on 07/May/18 $$\left.{a}\right)\:\:\:\:\:\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\:\frac{\left(\mathrm{cos}\:{x}+\mathrm{sin}\:{x}\right)^{\mathrm{3}} −\mathrm{2}\sqrt{\mathrm{2}}}{\mathrm{1}−\mathrm{sin}\:\mathrm{2}{x}}\:=? \\ $$$$\left.{b}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{sin}\:{x}\right)^{\frac{\mathrm{1}}{{x}}} \:=\:? \\ $$ Commented by abdo mathsup 649 cc…
Question Number 34522 by rahul 19 last updated on 07/May/18 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{log}\:_{{e}} \left\{\frac{\mathrm{sin}\:\left({a}+\frac{\mathrm{1}}{{x}}\right)}{\mathrm{sin}\:{a}}\right\}^{{x}} ,\:\mathrm{0}<{a}<\frac{\pi}{\mathrm{2}}\:. \\ $$ Commented by rahul 19 last updated on 08/May/18 $$?…
Question Number 34516 by rahul 19 last updated on 07/May/18 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{log}\:_{\mathrm{tan}\:^{\mathrm{2}} {x}} \left(\mathrm{tan}\:^{\mathrm{2}} \mathrm{2}{x}\right)\:=\:? \\ $$ Commented by math khazana by abdo last updated…
Question Number 100036 by bobhans last updated on 24/Jun/20 $$\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\sqrt{\mathrm{1}+\mathrm{sin}\:\mathrm{2x}}−\sqrt{\mathrm{1}−\mathrm{2sin}\:\mathrm{x}}}{\mathrm{x}} \\ $$$$\mathrm{g}\left(\mathrm{x}\right)\:=\:\mathrm{2x}+\:\sqrt{\mathrm{2x}}\:.\:\mathrm{find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{g}\left(\mathrm{f}\left(\mathrm{x}\right)\right) \\ $$ Answered by john santu last updated on 24/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{g}\left(\mathrm{f}\left(\mathrm{x}\right)\right)\:=\:\mathrm{g}\left(\underset{{x}\rightarrow\mathrm{0}}…
Question Number 100037 by bobhans last updated on 24/Jun/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{x}\sqrt{\mathrm{x}}\:\mathrm{sin}\:\left(\mathrm{2x}\right)\:? \\ $$ Commented by bramlex last updated on 24/Jun/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}\sqrt{{x}}\:=\:\infty\:\wedge\:−\mathrm{1}\leqslant\:\mathrm{sin}\:\mathrm{2}{x}\:\leqslant\:\mathrm{1} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}{x}\sqrt{{x}}\:\mathrm{sin}\:\mathrm{2}{x}\:=\:\infty\:…
Question Number 100027 by bemath last updated on 24/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{xsin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\:?\: \\ $$ Commented by john santu last updated on 24/Jun/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\mathrm{x}\:=\:\mathrm{0}\:\&\:−\mathrm{1}\leqslant\mathrm{sin}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\leqslant\mathrm{1} \\ $$$$\mathrm{then}\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 34464 by rahul 19 last updated on 06/May/18 $$\boldsymbol{{E}}{valuate}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:{x}^{{m}\:} \left({log}\:{x}\:\right)^{{n}} \:,\:{m},{n}\:\in\:\mathbb{N} \\ $$ Answered by MJS last updated on…
Question Number 34458 by rahul 19 last updated on 06/May/18 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}\:−\mathrm{sin}\:\left(\mathrm{sin}\:{x}\right)}{{x}^{\mathrm{3}} }\:=\:? \\ $$ Commented by math khazana by abdo last updated on 06/May/18…