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Rationalization Method to Remove Indeterminate Form

Evaluate: l...

Question

Evaluate: ${lim}_{x \to 1} \frac{3 x^{3} + 5 x - 8}{2 x^{3} + x - 3}$

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Solution

$lim x \to 1 \frac{3 x^{3} + 5 x - 8}{2 x^{3} + x - 3}$

Using L-Hospital rule

$lim x \to 1 \frac{9 x^{2} + 5}{6 x^{2} + 1}$

$\frac{9 (1) + 5}{6 (1) + 1} = \frac{14}{7}$

$= 2$ .

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