Evaluate the limit, if it exists. lim[h → 0] (√(9 + h) − 3)/h

Answer 1

If you meant lim (1/h) [sqrt(9-h) - 3]/h as h goes to 0, the limit is - 1/6

How come? By the binomial theorem:

sqrt(9-h) = 3 sqrt(1-h/9) = 3[1 - (1/2)(h/9) + terms of higher order in h].