### Home > CALC > Chapter 3 > Lesson 3.4.2 > Problem 3-168

3-168.

Evaluate each limit. If the limit does not exist, say so but also state if is approaching positive or negative infinity.

This is Ana's definition of the derivative:

That means

Findand then the limit will equal.Or you could multiply the numerator and denominator by the conjugate of the numerator.

Evaluate. The denominator will not equal zero so the limit and the actual value agree at

.

Rewrite the absolute value as a piecewise function but, since

, only consider the piece in which.

Think about what the graph of

looks like. What does it look like all the way to the right, as? How does theaffect the graph?