Home > CALC > Chapter Ch3 > Lesson 3.4.2 > Problem 3-168
3-168.
Evaluate each limit. If the limit does not exist, say so but also state if
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 the affect the graph?