Question

Evaluate the limit, if it exists.
lim (sqrt(x+2) -3)/(x-7)
(x -> 7)

I tried multiplying the numberator and denominator by the conjugate of the numberator (sqrt(x+2) +3) but, unless I multiplied wrong, I still ended up getting 0/0, when my calculator and the book say that I should get an answer of 1/6. Is this the wrong way to approach the problem?

Answer 1

You multiplied wrong.

You should have gotten in the numberator

x+2-9= x-7, which divides out the x-7 in the denominator, leaveing (sqrt(x+2) + 3), or 1/6

Answer 2

Ah, ok. I multiplied the (x-7) out in the denominator and must have multiplied wrong. Thank you!