Processing math: 0%
Home / Aptitude Tests / Further Mathematics / Find \(\lim\limits_{...
Find \(\lim\limits_{x \to 3} (\frac{x^{3} + x^{2} - 12x}{x^{...

Find lim

A.

\frac{7}{2}

B.

0

C.

\frac{-7}{2}

D.

-7

Correct answer is A

\lim\limits_{x \to 3} (\frac{x^{3} + x^{2} - 12x}{x^{2} - 9}) = \lim\limits_{x \to 3} (\frac{x^{3} - 3x^{2} + 4x^{2} - 12x}{(x - 3)(x + 3)}

\lim\limits_{x \to 3} (\frac{(x^{2} + 4x)(x - 3)}{(x - 3)(x + 3)} = \lim\limits_{x \to 3} (\frac{x^{2} + 4x}{x + 3})

=\frac{3^{2} + 4(3)}{3 + 3} = \frac{21}{6} = \frac{7}{2}