Question

Помогите вычислить пределы когда lim x→-2

Answer 1

a)

$\lim_{x \to -2} \dfrac{2x^2 + 3x + 1 }{2x^2 + 5x + 3} = \lim_{x \to -2} \dfrac{2x^2 + 2x + x + 1}{2x^2 + 2x + 3x + 3} = \\ \\ = \lim_{x \to -2}\dfrac{2x(x + 1) + (x + 1)}{2x(x + 1) + 3(x + 1)} = \lim_{x \to -2}\dfrac{(2x + 1)(x + 1)}{(2x + 3)(x + 1)} = \\ \\ =\lim_{x \to -2}\dfrac{2x + 1}{2x + 3} = \dfrac{-4 + 1}{-4 + 3} = 3$