limx→32x2+x−21x−3\lim\limits_{x \to 3} \frac{2x^{2}+x-21}{x-3}x→3limx−32x2+x−21
2x2+x−21=2x2−6x+7x−212x^{2} + x - 21 = 2x^{2} - 6x + 7x - 212x2+x−21=2x2−6x+7x−21 (by factorizing)
= (2x+7)(x−3)(2x + 7)(x - 3)(2x+7)(x−3)
∴limx→32x2+x−21x−3≡limx→3(2x+7)(x−3)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}∴x→3limx−32x2+x−21≡x→3limx−3(2x+7)(x−3)
limx→3(2x+7)=2(3)+7=13\lim\limits_{x \to 3} (2x + 7) = 2(3) + 7 = 13x→3lim(2x+7)=2(3)+7=13
