Question and Answers Forum

All Questions      Topic List

None Questions

Previous in All Question      Next in All Question      

Previous in None      Next in None      

Question Number 81970 by arkanmath7@gmail.com last updated on 17/Feb/20

$$findthelimitasn->\mathrm{\infty }$$ $$$$ $$lim{(2-{}^n\sqrt{x})}^n$$ $$$$

Commented bymsup trace by abdo last updated on 17/Feb/20

$$letf\left(x\right)={\left(2{-}^n\sqrt{x}\right)}^n\Rightarrow$$ $$f\left(x\right)=e^{nln\left(2{-}^n\sqrt{x}\right)}$$ $$=e^{nln\left(2\right)+ln(1-\frac{1}{2}{e}^{\frac{1}{n}ln\left(x\right)})}$$ $$=e^{nln\left(2\right)}\times e^{ln(1-\frac{1}{2}{e}^{\frac{lnx}{n}})}\to +\mathrm{\infty }$$ $$because{lim}_{n\to +\mathrm{\infty }}{e}^{nln\left(2\right)}=+\mathrm{\infty }$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com