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)}} \:=? \\ $$ Answered by bemath last updated on 10/Oct/20 Terms of…
Question Number 117164 by bobhans last updated on 10/Oct/20 $$\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{n}+\mathrm{9}}{\mathrm{2n}−\mathrm{1}}\right)^{\mathrm{n}} =? \\ $$ Answered by bemath last updated on 10/Oct/20 $$\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\mathrm{2n}−\mathrm{1}+\mathrm{10}−\mathrm{n}}{\mathrm{2n}−\mathrm{1}}\right)^{\mathrm{n}} = \\…
Question Number 51617 by Saorey last updated on 29/Dec/18 $$\mathrm{A}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{{x}} −{e}^{−{x}} −\mathrm{2}{x}}{{x}^{\mathrm{3}} }\left({without}\:\right. \\ $$$$\left.{using}\:{L}'\mathrm{hopital}\:\mathrm{rule}\right) \\ $$$$ \\ $$ Commented by aseerimad last updated…
Question Number 117147 by bemath last updated on 10/Oct/20 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{\mathrm{cosh}\:\left(\mathrm{2x}\right)}{\mathrm{cosh}\:\left(\mathrm{x}\right)}\right)^{\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }} \:=? \\ $$ Answered by Olaf last updated on 10/Oct/20 $$\mathrm{cosh}{u}\:\underset{\mathrm{0}} {\sim}\:\mathrm{1}+\frac{{u}^{\mathrm{2}} }{\mathrm{2}}…
Question Number 182659 by mathlove last updated on 12/Dec/22 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt[{{n}}]{{n}!}}{{n}}=? \\ $$ Answered by Frix last updated on 12/Dec/22 $${n}!\sim\frac{{n}^{{n}} \sqrt{\mathrm{2}\pi{n}}}{\mathrm{e}^{{n}} } \\ $$$$\underset{{n}\rightarrow\infty}…
Question Number 182649 by amin96 last updated on 12/Dec/22 $$\boldsymbol{{f}}\left(\boldsymbol{{x}};\boldsymbol{{y}}\right)=\frac{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} }{\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{4}} }\:\:\:\:\: \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\underset{{y}\rightarrow\mathrm{0}} {\mathrm{lim}}\boldsymbol{{f}}\left(\boldsymbol{{x}};\boldsymbol{{y}}\right)\right)=? \\ $$$$\underset{\boldsymbol{{y}}\rightarrow\infty} {\mathrm{lim}}\left(\underset{{x}\rightarrow\infty} {\mathrm{lim}}\boldsymbol{{f}}\left(\boldsymbol{{x}};\boldsymbol{{y}}\right)\right)=? \\ $$ Answered…