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

3-168.

Evaluate each limit. If the limit does not exist due to a vertical asymptote, then add an approach statement stating if is approaching negative or positive infinity.

This is Ana's definition of the derivative:

That means

and . Find

and 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?