belicoloVgaby belicoloVgaby

21-11-2016
Mathematics

Answered

find a value of the constant k such that the limit exists:

lim (x^2+4x+k)/(x+2) as x goes to -2 ...?

Verified Answer :

alsteva alsteva

22-11-2016

\(\lim_{x \to -2} \frac{x^2+4x+k}{x+2}\)

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

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

Therefore, k = 4.

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