Question and Answers Forum

All Questions      Topic List

Limits Questions

Previous in All Question      Next in All Question      

Next in Limits      

Question Number 222 by 123456 last updated on 25/Jan/15

lim_(x→0) ((sin x)/(arcsin x))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{sin}\:{x}}{\mathrm{arcsin}\:{x}} \\ $$

Answered by ghosea last updated on 16/Dec/14

lim_(x→0)  ((sin x)/(arcsin x))  =lim_(x→0)  ((sin x)/x)∙(x/(arcsin x))  =lim_(x→0)  ((sin x)/x)∙lim_(x→0)  (x/(arcsin x))  =1∙1=1

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{\mathrm{arcsin}\:{x}} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{{x}}\centerdot\frac{{x}}{\mathrm{arcsin}\:{x}} \\ $$$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:{x}}{{x}}\centerdot\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}}{\mathrm{arcsin}\:{x}} \\ $$$$=\mathrm{1}\centerdot\mathrm{1}=\mathrm{1} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com