Question Number 12492 by shardon last updated on 23/Apr/17 $${this}\:{is}\:{calculus}\: \\ $$$${evaluate}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{sin}\mathrm{3}{xsin}\mathrm{5}{x}}{\mathrm{7}{x}^{\mathrm{2}} } \\ $$ Commented by shardon last updated on 23/Apr/17 $${what}\:{happen}\:{to}\:{the}\:{x}^{\mathrm{2}} \\…
Question Number 12495 by shardon last updated on 23/Apr/17 $${find}\:{the}\:{real}\:{values}\:{of}\:{x}\:{for}\:{which} \\ $$$${the}\:{function}\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{2}} \\ $$$$ \\ $$ Commented by mrW1 last updated on 23/Apr/17…
Question Number 78012 by malwaan last updated on 13/Jan/20 $$\boldsymbol{{prove}}\:\boldsymbol{{that}} \\ $$$$\underset{\boldsymbol{{x}}\rightarrow\mathrm{1}} {\boldsymbol{{lim}}}\frac{\boldsymbol{{sin}}\left(\boldsymbol{\pi{cos}\pi{x}}\right)}{\left(\boldsymbol{{x}}−\mathrm{1}\right)^{\mathrm{2}} }\:=\:−\:\frac{\boldsymbol{\pi}^{\mathrm{3}} }{\mathrm{2}} \\ $$ Commented by msup trace by abdo last updated…
Question Number 78021 by jagoll last updated on 13/Jan/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\left[\underset{\frac{\pi}{\mathrm{3}}} {\int}^{{x}^{\mathrm{2}} +\frac{\pi}{\mathrm{3}}} \frac{\mathrm{cos}\:{x}}{{x}}\:{dx}\:\right]\:= \\ $$ Commented by mr W last updated on 13/Jan/20…
Question Number 143532 by bramlexs22 last updated on 15/Jun/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\mathrm{cos}\:{x}}{\mathrm{tan}\:^{\mathrm{4}} {x}}\:=? \\ $$ Answered by mathmax by abdo last updated on 15/Jun/21 $$\mathrm{cosx}\sim\mathrm{1}−\frac{\mathrm{x}^{\mathrm{2}}…
Question Number 143531 by bramlexs22 last updated on 15/Jun/21 $$\:\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\frac{\mathrm{2}\sqrt{{x}}+\mathrm{3}\:\sqrt[{\mathrm{3}}]{{x}}\:+\mathrm{5}\:\sqrt[{\mathrm{5}}]{{x}}}{\:\sqrt{\mathrm{3}{x}−\mathrm{2}}\:+\sqrt[{\mathrm{3}}]{\mathrm{2}{x}−\mathrm{3}}}\:=? \\ $$ Answered by bobhans last updated on 15/Jun/21 Terms of Service Privacy Policy…
Question Number 143453 by yahy last updated on 14/Jun/21 Answered by Willson last updated on 14/Jun/21 $$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}^{\:\:\:\:\mathrm{n}} }\sqrt{\frac{\mathrm{n}^{\mathrm{n}} }{\mathrm{n}!}}\:=\:\frac{\mathrm{1}}{{e}} \\ $$ Commented by yahy…
Question Number 12382 by tawa last updated on 21/Apr/17 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\:\frac{\mathrm{ln}\:\mathrm{cos}\left(\mathrm{3x}\right)}{\mathrm{ln}\:\mathrm{cos}\left(\mathrm{2x}\right)} \\ $$ Answered by ajfour last updated on 21/Apr/17 $$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left[\mathrm{1}−\left(\mathrm{1}−\mathrm{cos}\:\mathrm{3}{x}\right)\right]}{\mathrm{ln}\:\left[\mathrm{1}−\left(\mathrm{1}−\mathrm{cos}\:\mathrm{2}{x}\right)\right]} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left[\mathrm{1}−\mathrm{2sin}\:^{\mathrm{2}}…
Question Number 143428 by mnjuly1970 last updated on 14/Jun/21 $$\:\:\:\:\: \\ $$$$…{Advanced}\:……{Mathematics}… \\ $$$$\:\:\:\:\:{Evaluate}:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\boldsymbol{\phi}\::=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{coth}\left(\pi{n}\right)}{{n}^{\mathrm{3}} }\:=? \\ $$ Answered by mindispower last…
Question Number 77856 by walidMTS last updated on 11/Jan/20 $$\underset{{x}\rightarrow\mathrm{0}} {{l}im}\left(\frac{{e}^{{x}} −{x}−\mathrm{1}}{{x}}\right) \\ $$ Commented by mathmax by abdo last updated on 11/Jan/20 $${we}\:{have}\:{e}^{{x}} =\sum_{{n}=\mathrm{0}}…