### Home > CALC > Chapter Ch3 > Lesson 3.4.2 > Problem 3-168

3-168.

This is Ana's definition of the derivative:

Find *f* '(*x*) and then the limit will equal *f* '(0).

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 *x* = 2.

Rewrite the absolute value as a piecewise function but, since *x* → 2^{+}, only consider the piece in which *x* > 2.

Think about what the graph of *y* = *e*^{−}* ^{x}* looks like. What does it look like all the way to the right, as

*x*→ ∞? How does the +1 affect the graph?