If there is a number $a$ such that
$$\lim_{x \to -2}\frac{3x^2 + ax + a + 3}{x^2 + x -2}$$ exists. Find the value of $a$ and the value of the limit.
Find the value of $a$ and the value of the limit
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calculus
1 Answers
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When $x = -2$ the function is undefined so (x+2) must be a factor of both the numerator and denominator.
Numerator(-2) = 0
$$ 3(4) + (-2a) + a + 3 = 0 : a = 15$$
$$\lim_{x \to -2}\frac{3x^2 + 15x + 18}{x^2 + x -2} = \lim_{x \to -2}\frac{(x+2)(3x+9)}{(x+2)(x-1)} = \lim_{x \to -2}\frac{(3x+9)}{(x-1)} = -1$$