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 101075 by bemath last updated on 30/Jun/20

lim_(x→0)  ((arcsin (x^2 )−x^2 )/(x^4  tan^2 x)) = ?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{arcsin}\:\left(\mathrm{x}^{\mathrm{2}} \right)−\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{4}} \:\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}}\:=\:? \\ $$

Commented by Dwaipayan Shikari last updated on 30/Jun/20

lim_(x→0) ((x^2 +(x^6 /6)−x^2 )/(x^4 .x^2 )) =((x^6 /6)/x^6 )=(1/6)  {As x→0   suppose tanx=x   tan^2 x=x^2 }{And maclaurin series for sin^(−1) x^2 }

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} +\frac{{x}^{\mathrm{6}} }{\mathrm{6}}−{x}^{\mathrm{2}} }{{x}^{\mathrm{4}} .{x}^{\mathrm{2}} }\:=\frac{\frac{{x}^{\mathrm{6}} }{\mathrm{6}}}{{x}^{\mathrm{6}} }=\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$\left\{{As}\:{x}\rightarrow\mathrm{0}\:\:\:{suppose}\:{tanx}={x}\:\:\:{tan}^{\mathrm{2}} {x}={x}^{\mathrm{2}} \right\}\left\{{And}\:{maclaurin}\:{series}\:{for}\:\mathrm{sin}^{−\mathrm{1}} {x}^{\mathrm{2}} \right\} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com