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Question Number 15195 by Joel577 last updated on 08/Jun/17

$$\underset{x\to \mathrm{\infty }}{\lim }{\left(\frac{2x-5}{2x+1}\right)}^{x+3}$$

Commented by Joel577 last updated on 08/Jun/17

$$=\underset{x\to \mathrm{\infty }}{\lim }{(1-\frac{6}{2x+1})}^{x+3}$$$$=\underset{x\to \mathrm{\infty }}{\lim }{\left\{{\left[{(1-\frac{6}{2x+1})}^{-\frac{2x+1}{6}}\right]}^{-\frac{6}{2x+1}}\right\}}^{x+3}$$$$={\left[\underset{x\to \mathrm{\infty }}{\lim }{(1-\frac{6}{2x+1})}^{-\frac{2x+1}{6}}\right]}^{\underset{x\to \mathrm{\infty }}{\lim }(-\frac{6(x+3)}{2x+1})}$$$$=e^{-3}$$$$$$$$\mathrm{Is}\mathrm{it}\mathrm{correct}?$$

Commented by Joel577 last updated on 08/Jun/17

$$thankyouverymuch$$

Commented by mrW1 last updated on 08/Jun/17

$$\mathrm{correct}!$$

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