### Home > CALC3RD > Chapter Ch5 > Lesson 5.4.1 > Problem 5-143

5-143.

Evaluate each of the following limits.

You could evaluate this limit algebraically.

Recall that:

Or you could recognize that this is Ana's Definition of the Derivative.

So theYou should recognize that this is Hanah's Definition of the Derivative.

Deconstruct Hanah's definition.

1. Determine what is.

2. Find its derivative. That is the value of the limit.This is Hana's Definition of the Derivative, evaluated at

This is Ana's Definition of the Derivative, evaluated at

.This limit could be rewritten as

Of course,

. What do all of the limits above have in common?

Refer to hints above.