belicoloVgaby belicoloVgaby
  • 21-11-2016
  • Mathematics
contestada

find a value of the constant k such that the limit exists:
lim (x^2+4x+k)/(x+2) as x goes to -2 ...?

Respuesta :

alsteva alsteva
  • 22-11-2016
[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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