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Question

Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)

lim h→0 (9 + h)−1 − 9−1

h

Answer 1

lim h→0 (9 + h)−1 − 9−1

As h goes to 0, 9 + h is going to approach 9. So (9+h)^(-1) will approach 9^(-1) or 1/9. So the entire expression will approach 1/9 - 1/9 or 0.

Answer 2

The limit is 0...and when x approaches 0 from above the function approaches zero from below also.; that is sometimes written 0^-.