Question Number 117498 by bobhans last updated on 12/Oct/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\left(\mathrm{x}−\mathrm{sin}\:\mathrm{x}\right)}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }−\mathrm{1}}\:? \\ $$ Answered by bemath last updated on 12/Oct/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:\left(\mathrm{x}−\mathrm{sin}\:\mathrm{x}\right)}{\:\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{3}} }−\mathrm{1}}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{x}−\left(\mathrm{x}−\frac{\mathrm{x}^{\mathrm{3}}…
Question Number 182978 by TUN last updated on 18/Dec/22 Answered by dumitrel last updated on 18/Dec/22 $$ \\ $$ Commented by dumitrel last updated on…
Question Number 117422 by bemath last updated on 11/Oct/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3tan}\:\mathrm{4x}−\mathrm{4tan}\:\mathrm{3x}}{\mathrm{3sin}\:\mathrm{4x}−\mathrm{4sin}\:\mathrm{3x}}\:=? \\ $$ Answered by bobhans last updated on 11/Oct/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3tan}\:\mathrm{4x}−\mathrm{4tan}\:\mathrm{3x}}{\mathrm{3sin}\:\mathrm{4x}−\mathrm{4sin}\:\mathrm{3x}}\:=\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{3}\left(\mathrm{4x}+\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{4x}\right)^{\mathrm{3}}…
Question Number 117416 by Lordose last updated on 11/Oct/20 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } −\mathrm{cosx}}{\mathrm{sin}^{\mathrm{2}} \mathrm{x}} \\ $$ Answered by Olaf last updated on 11/Oct/20 $$\forall{x}\in\mathbb{R},\:\mathrm{sin}{x}\:\leqslant\:{x}\:\Rightarrow\:\frac{\mathrm{1}}{\mathrm{sin}^{\mathrm{2}} {x}}\:\geqslant\:\frac{\mathrm{1}}{{x}^{\mathrm{2}}…
Question Number 117417 by bobhans last updated on 11/Oct/20 $$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\left(\mathrm{tanh}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)−\frac{\mathrm{1}}{\mathrm{cosh}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} =? \\ $$ Answered by Lordose last updated on 11/Oct/20 $$\mathrm{1} \\ $$…
Question Number 117412 by bobhans last updated on 11/Oct/20 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{6}}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{2sin}\:\mathrm{x}}{\:\mathrm{1}−\sqrt{\mathrm{3}}\:\mathrm{tan}\:\mathrm{x}}\:=\:? \\ $$ Commented by Lordose last updated on 11/Oct/20 $$\mathrm{you}\:\mathrm{edited}\:\mathrm{the}\:\mathrm{question}.? \\ $$ Commented by…
Question Number 182836 by mathlove last updated on 15/Dec/22 Answered by floor(10²Eta[1]) last updated on 15/Dec/22 $$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\mathrm{2}^{\mathrm{x}} \mathrm{ln2}+\mathrm{3}^{\mathrm{x}} \mathrm{ln3}+\mathrm{4}^{\mathrm{x}} \mathrm{ln4}}{\mathrm{1}+\mathrm{2x}+\mathrm{3x}^{\mathrm{2}} +\mathrm{4x}^{\mathrm{3}} }=\frac{\mathrm{4ln2}+\mathrm{9ln3}+\mathrm{16ln4}}{\mathrm{1}+\mathrm{4}+\mathrm{12}+\mathrm{32}} \\ $$$$=\frac{\mathrm{36ln2}+\mathrm{9ln3}}{\mathrm{49}}…
Question Number 182797 by universe last updated on 14/Dec/22 $$\:\mathrm{find}\:\:\mathrm{the}\:\mathrm{max}\:\mathrm{and}\:\:\mathrm{min}\:\mathrm{value} \\ $$$$\:\mathrm{f}\left(\mathrm{x},\mathrm{y},\mathrm{z}\right)\:=\:\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} +\mathrm{z}^{\mathrm{3}} −\mathrm{9xy}−\mathrm{9xz}+\mathrm{27x} \\ $$ Commented by mahdipoor last updated on 14/Dec/22 $$\pm\infty…
Question Number 182770 by mathlove last updated on 14/Dec/22 Answered by ARUNG_Brandon_MBU last updated on 14/Dec/22 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\pi}{{n}}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{sin}\left(\frac{{k}\pi}{{n}}\right)=\pi\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{sin}\left(\pi{x}\right){dx}=\mathrm{2} \\ $$ Terms…
Question Number 117171 by bemath last updated on 10/Oct/20 $$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{1}+\mathrm{x}\:\mathrm{tan}^{−\mathrm{1}} \left(\mathrm{x}\right)}{\mathrm{cosh}\:\left(\mathrm{x}\right)}\right)^{\frac{\mathrm{1}}{\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{x}\right)}} \:=? \\ $$ Answered by bemath last updated on 10/Oct/20 Terms of…