Find (limlimits_{x to 3} (frac{x^{3} + x^{2} – 12x}{x^{2} – 9}))
-
A.
(frac{7}{2}) -
B.
(0) -
C.
(frac{-7}{2}) -
D.
(-7)
Correct Answer: Option A
Explanation
(limlimits_{x to 3} (frac{x^{3} + x^{2} – 12x}{x^{2} – 9}) = limlimits_{x to 3} (frac{x^{3} – 3x^{2} + 4x^{2} – 12x}{(x – 3)(x + 3)})
(limlimits_{x to 3} (frac{(x^{2} + 4x)(x – 3)}{(x – 3)(x + 3)} = limlimits_{x to 3} (frac{x^{2} + 4x}{x + 3}))
=(frac{3^{2} + 4(3)}{3 + 3} = frac{21}{6} = frac{7}{2})