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  4. displaystyle lim x arrow ∞ (3.2n+1-4.5n+1/5.2n+7.5n)=

Q. $\displaystyle\lim _{x \rightarrow \infty} \frac{3.2^{n+1}-4.5^{n+1}}{5.2^{n}+7.5^{n}}=$

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Solution:

$\displaystyle\lim _{n \rightarrow \infty} \frac{3 \cdot 2^{n+1}-4.5^{n+1}}{5.2^{n}+7.5^{n}}$
$=\displaystyle\lim _{n \rightarrow \infty} \frac{5^{n}\left(3 \cdot \frac{2^{n}}{5^{n}} \cdot 2-4.5\right)}{5^{n}\left(5 \cdot \frac{2^{n}}{5^{n}}+7\right)}$
$=\frac{0-20}{0+7}=-\frac{20}{7}$

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