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 90226 by manuel__ last updated on 22/Apr/20

$$\underset{x\to 0}{\lim }\left(\frac{x^3(e^x-1)-x^2}{{xe}^x-x}\right)=?$$

Commented by john santu last updated on 22/Apr/20

$$\underset{x\to 0}{\lim }\frac{x^2(e^x-1)-x}{e^x-1}=$$$$\underset{x\to 0}{\lim }\frac{2x(e^x-1)+x^2{e}^x-1}{e^x}=-1$$

Commented by mathmax by abdo last updated on 22/Apr/20

$$letf\left(x\right)=\frac{x^3(e^x-1)-x^2}{{xe}^x-x}\Rightarrow f\left(x\right)=\frac{x^2(e^x-1)-x}{e^x-1}$$$$e^x\sim 1+x\Rightarrow x^2(e^x-1)-x\sim x^3-x\Rightarrow f\left(x\right)\sim \frac{x^3-x}{x}=x^2-1\Rightarrow$$$${lim}_{x\to 0}f\left(x\right)=-1$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com