Given x→3limx^3 x^2 18x 3 = x→3lim(x 3)(x^2+2x+6)x 3 = x→3lim(x^2+2x+6) Put limit = 3^2+2(3)+6 = 9+6+6 =21 ...

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Factorization Method Form to Remove Indeterminate Form

limx → 3x3-x2...

Question

$l i m_{x \to 3} \frac{x^{3} - x^{2} - 18}{x - 3} .$

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Solution

Given $l i m x \to 3 \frac{x^{3} - x^{2} - 18}{x - 3}$
$= l i m x \to 3 \frac{(x - 3) (x^{2} + 2 x + 6)}{x - 3}$
$= l i m x \to 3 (x^{2} + 2 x + 6)$
Put limit
$= 3^{2} + 2 (3) + 6$
$= 9 + 6 + 6$
$= 21$

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