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 129387 by Study last updated on 15/Jan/21

$$li\underset{x\to 0}{m}{\left(cosx\right)}^{logx}=???$$

Commented by Study last updated on 15/Jan/21

$$whowillsolve?$$

Answered by mindispower last updated on 15/Jan/21

$$=e^{ln\left(x\right)ln\left(cos\left(x\right)\right)}$$$$ln\left(cos\left(x\right)\right)=ln(1-\frac{x^2}{2}+o\left(x^2\right))=-\frac{x^2}{2}+o\left(x^2\right)$$$$=e^{ln\left(x\right)(-\frac{x^2}{2}+o\left(x^2\right))}$$$$\underset{x\to 0}{\lim }{x}^{2}ln\left(x\right)=0$$$$weget{e}^0=1$$

Commented by Study last updated on 16/Jan/21

$$ithinktoundefined?$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com