\(\lim\limits_{x \to 3} \frac{2x^{2} + x - 21}{x - 3}\)

\(2x^{2} + x - 21 = 2x^{2} - 6x + 7x - 21 \) (by factorizing)

= \((2x + 7)(x - 3)\)

\(\therefore \lim\limits_{x \to 3} \frac{2x^{2} + x - 21}{x - 3} \equiv \lim\limits_{x \to 3} \frac{(2x+7)(x-3)}{x-3}\)

\(\lim\limits_{x \to 3} (2x + 7)  = 2(3) + 7 = 13\)