evaluate, Limits

Question

Evaluate the following limit if it exists or show that it does not exist.

lim h→0 ((√h + 9) − 3) /h

h+9 is under the root

Answer 1

desmos.com/calculator/8tzh24dfxq

Answer 2

This question is most easily solved with L'Hopital's rule: Since simply plugging in h=0 gives us an undefined limit (0/0), we can replace the numerator and denominator with their respective derivatives to get 1/[2√(h+9)] in the numerator and 1 in the denominator. We can plug in h=0 to this new fraction to find that the limit is (1/6)/1 = 1/6.