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Question Number 28097 by tawa tawa last updated on 20/Jan/18

$$\underset{x\to \mathrm{\infty }}{\lim }\frac{3^{\mathrm{x}}-2^{\mathrm{x}}}{{\mathrm{x}}^2}$$

Commented by abdo imad last updated on 20/Jan/18

$$={lim}_{x\to +\propto }\frac{3^x(1-{\left(\frac{2}{3}\right)}^x)}{x^2}={lim}_{x\to +\propto }\frac{3^x}{x^2}$$$$={lim}_{x\to +\propto }{e}^{xln3}{e}^{-2lnx}={lim}_{x\to +\propto }{e}^{x(ln3-2\frac{lnx}{x})}$$$$={lim}_{x\to +\propto }{e}^{xln3}=+\propto because{lim}_{x\to \propto }{\left(\frac{2}{3}\right)}^x=0$$$$and{lim}_{x\to +\propto }\frac{lnx}{x}=0.$$

Commented by çhëý böý last updated on 20/Jan/18

$$Goodworksir$$$$$$

Commented by tawa tawa last updated on 21/Jan/18

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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