Question

Evaluate $\underset{x\to 2}{lim}\frac{7x^2-11x-6}{3x^2-x-10}$

• A. $\frac{17}{11}$
• B. $\frac{11}{17}$
• C. $\frac{17}{14}$
• D. $-\frac{17}{11}$

Answer 1

The correct option is A $\frac{17}{11}$

$\underset{x\to 2}{lim}\frac{7x^2-11x-6}{3x^2-x-10}$

$=\underset{x\to 2}{lim}\frac{(x-2)(7x+3)}{(x-2)(3x+5)}$

$=\underset{x\to 2}{lim}\frac{7x+3}{3x+5}$

$=\frac{7\left(2\right)+3}{3\left(2\right)+5}$

$=\frac{17}{11}$