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 81558 by john santu last updated on 14/Feb/20

$$\underset{x\to \mathrm{\infty }}{\lim }\frac{{\mathrm{e}}^{\mathrm{x}}+\cos \mathrm{x}+\ln ({\mathrm{x}}^2-2\mathrm{x}+3)}{\mathrm{x}}=$$

Commented by malwaan last updated on 14/Feb/20

$$\mathrm{\infty }$$

Commented by mathmax by abdo last updated on 14/Feb/20

$$f\left(x\right)=\frac{e^x+cosx+ln(x^2-2x+3)}{x}\Rightarrow forx\to +\mathrm{\infty }$$$$f\left(x\right)=\frac{e^x+cosx+2lnx+ln(1-\frac{2}{x}+\frac{3}{x^2})}{x}$$$$\sim \frac{e^x+cosx+2lnx+(-\frac{2}{x}+\frac{3}{x^2})}{x}=\frac{e^x}{x}+\frac{cosx}{x}+\frac{2lnx}{x}-\frac{2}{x^2}+\frac{3}{x^3}$$$$nowitsclearthat{lim}_{x\to +\mathrm{\infty }}f\left(x\right)=+\mathrm{\infty }$$$$for-\mathrm{\infty }f\left(x\right)\sim \frac{e^x}{x}+\frac{cosx}{x}+\frac{2ln(-x)}{x}-\frac{2}{x^2}+\frac{3}{x^3}\Rightarrow$$$${lim}_{x\to -\mathrm{\infty }}f\left(x\right)=0$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com