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 78682 by Omer Alattas last updated on 19/Jan/20

Commented by mathmax by abdo last updated on 19/Jan/20

$$wehave{\left(sinx\right)}^x=e^{xln\left(sinx\right)}andxln\left(sinx\right)\sim xlnx(x\to 0)\Rightarrow$$$${lim}_{x\to 0^{+}}xln\left(sinx\right)=0\Rightarrow {lim}_{x\to 0^{+}}{\left(sinx\right)}^x=e^0=1$$

Commented by john santu last updated on 20/Jan/20

$$lety=\underset{x\to 0^{+}}{\lim }{\left(\sin x\right)}^x$$$$ln\left(y\right)=\underset{x\to 0^{+}}{\lim }xln\left(\sin x\right)$$$$=\underset{x\to 0^{+}}{\lim }\frac{ln\left(\sin x\right)}{x^{-1}}=\underset{x\to 0^{+}}{\lim }\frac{\cot x}{-x^{-2}}$$$$=\underset{x\to 0^{+}}{\lim }\frac{-x^2}{\tan x}=0$$$$finallyweget{e}^{ln\left(y\right)}=e^0\Rightarrow y=1$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com