Chapter 4.2, Problem 54E

(a)

To determine

To Graph: The function $y=e^x$.

(b)

To determine

The region near $x=0$ until the curve $y=e^x$ appears as a straight line by zoom in and estimate its slope. This number is an estimate of $\frac{d}{dx}{e}^x$ at $x=0$. Compare the answer to the actual slope $1$.

(c)

To determine

The graph of the function $y=2^x$ and its slope near $x=0$, by zooming the curve until the curve $y=e^x$ appears as a straight line by zoom. Observe that the slope at $x=0$ is not $1$.