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Rationalization Method to Remove Indeterminate Form

Evaluate: l...

Question

Evaluate: $lim x \to \infty \frac{4 x - 3}{2 x + 3}$

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Solution

$lim x \to \infty \frac{4 x - 3}{2 x + 3} \Rightarrow lim x \to \infty \frac{(4 - 3 / x) x}{(2 + 3 / x) x}$
$[w h e n x \to \infty, \frac{1}{x} \to 0]$
$= \frac{(4 - 0)}{(2 - 0)} = 2$

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