Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 165372 by LEKOUMA last updated on 31/Jan/22

$$\underset{x\to +\mathrm{\infty }}{\lim ln}(1+2^x)\ln (1+\frac{3}{x})$$

Answered by Ar Brandon last updated on 31/Jan/22

$$\underset{x\to +\mathrm{\infty }}{\lim ln}(1+2^x)\ln (1+\frac{3}{x})$$$$=\underset{x\to +\mathrm{\infty }}{\lim }\frac{3}{x}\ln (1+2^x)$$$$=\underset{x\to +\mathrm{\infty }}{\lim }\frac{3}{x}({\ln 2}^x+\ln (1+2^{-x}))$$$$=\underset{x\to +\mathrm{\infty }}{\lim }\frac{3}{x}{\ln 2}^x+\underset{x\to +\mathrm{\infty }}{\lim }\frac{3}{x}\ln (1+2^{-x})$$$$=\underset{x\to +\mathrm{\infty }}{\lim 3ln2}+\underset{x\to +\mathrm{\infty }}{\lim }\frac{3}{x}\times 2^{-x}=3\ln 2$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com