Find (limlimits_{x to 3} frac{2x^{2} + x – 21}{x – 3}).
-
A.
0 -
B.
1 -
C.
7 -
D.
13
Correct Answer: Option D
Explanation
(limlimits_{x to 3} frac{2x^{2} + x – 21}{x – 3})
(2x^{2} + x – 21 = 2x^{2} – 6x + 7x – 21 ) (by factorizing)
= ((2x + 7)(x – 3))
(therefore limlimits_{x to 3} frac{2x^{2} + x – 21}{x – 3} equiv limlimits_{x to 3} frac{(2x+7)(x-3)}{x-3})
(limlimits_{x to 3} (2x + 7) = 2(3) + 7 = 13)