Question and Answers Forum

All Questions      Topic List

Limits Questions

Previous in All Question      Next in All Question      

Previous in Limits      Next in Limits      

Question Number 105114 by john santu last updated on 26/Jul/20

lim_(x→0) ((2−((1−sin ^2 (3x)))^(1/3) −((1−sin ^2 (2x)))^(1/3) )/x^2 )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}−\sqrt[{\mathrm{3}}]{\mathrm{1}−\mathrm{sin}\:\:^{\mathrm{2}} \left(\mathrm{3}{x}\right)}−\sqrt[{\mathrm{3}}]{\mathrm{1}−\mathrm{sin}\:\:^{\mathrm{2}} \left(\mathrm{2}{x}\right)}}{{x}^{\mathrm{2}} } \\ $$

Answered by bemath last updated on 26/Jul/20

lim_(x→0) ((2−(1−((sin ^2 (3x))/3))−(1−((sin ^2 (2x))/3)))/x^2 )  lim_(x→0) (((1/3)(sin ^2 (3x)+sin^2 (2x)))/x^2 ) =        →(1/3)(9+4) = ((13)/3)

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}−\left(\mathrm{1}−\frac{\mathrm{sin}\:\:^{\mathrm{2}} \left(\mathrm{3}{x}\right)}{\mathrm{3}}\right)−\left(\mathrm{1}−\frac{\mathrm{sin}\:\:^{\mathrm{2}} \left(\mathrm{2}{x}\right)}{\mathrm{3}}\right)}{{x}^{\mathrm{2}} } \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{sin}\:\:^{\mathrm{2}} \left(\mathrm{3}{x}\right)+\mathrm{sin}\:^{\mathrm{2}} \left(\mathrm{2}{x}\right)\right)}{{x}^{\mathrm{2}} }\:= \\ $$$$\:\:\:\:\:\:\rightarrow\frac{\mathrm{1}}{\mathrm{3}}\left(\mathrm{9}+\mathrm{4}\right)\:=\:\frac{\mathrm{13}}{\mathrm{3}} \\ $$

Answered by OlafThorendsen last updated on 26/Jul/20

lim_(x→0) ((2−((1−9x^2 ))^(1/3) −((1−4x^2 ))^(1/3) )/x^2 )  lim_(x→0) ((2−(1−3x^2 )−(1−(4/3)x^2 ))/x^2 )  = ((13)/3)

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}−\sqrt[{\mathrm{3}}]{\mathrm{1}−\mathrm{9}{x}^{\mathrm{2}} }−\sqrt[{\mathrm{3}}]{\mathrm{1}−\mathrm{4}{x}^{\mathrm{2}} }}{{x}^{\mathrm{2}} } \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}−\left(\mathrm{1}−\mathrm{3}{x}^{\mathrm{2}} \right)−\left(\mathrm{1}−\frac{\mathrm{4}}{\mathrm{3}}{x}^{\mathrm{2}} \right)}{{x}^{\mathrm{2}} } \\ $$$$=\:\frac{\mathrm{13}}{\mathrm{3}} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com