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

5-143.

Easy Limits

Evaluate each of the following limits. Homework Help ✎

What do all of the limits above have in common?

You could evaluate this limit algebraically.

Recall that: *x*^{3} − 8 = (*x* − 2)(*x*^{2} + 2*x* − 4)

Or you could recognize that this is Ana's Definition of the Derivative.*f*(*x*) = *x*^{3}*a* = 2

So the limit = *f* '(2)

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

Deconstruct Hanah's definition.

1. Determine what is *f*(*x*).

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 *x* = *π*.

This limit could be rewritten as

Of course, tan(5,*π*) = 0.

Refer to hints above.