Respuesta :

[tex] \lim_{x \to -2} \frac{x^2+4x+k}{x+2} [/tex]

We should eliminate (x+2) in the denominator.

[tex]\lim_{x \to -2} \frac{x^2+4x+k}{x+2} \\ \\ \lim_{x \to -2} \frac{x^2+4x+4}{x+2} \\ \\ \lim_{x \to -2} \frac{(x+2)^2}{x+2} \\ \\ \lim_{x \to -2} {(x+2)}=-2+2=0[/tex]

Therefore, k = 4.

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