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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?

2 answers

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