calculus evaluate the limit

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

We are not allowed to use L’hospital’s rule.

Answer 1

Answer 2

We can take this limit by just simplifying the fraction. Multiply the numerator and denominator by the factor [√(h+9) + 3] so that the numerator simplifies very nicely to h and the denominator is h[√(h+9) + 3].

Simplify by canceling the h from the numerator and denominator; we're left with 1/[√(h+9) + 3]. Now, we can plug in h=0 to get the answer 1/6.