Question

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

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

Answer 1

`\lim_(x \to -2) (x^2+4x+k)/(x+2)`

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


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

Therefore, k = 4.