Consider the function f(x)=(4^x−1)/x.

Question

(a) Fill in the following table of values for f(x):

x= -0.1 -0.01 -0.001 -0.0001 0.0001 0.001 0.01 0.1
f(x)=
I the the falues of f(x) for each interval...

(b) Based on your table of values, what would you expect the limit of f(x) as x approaches zero to be?
limx->0 (4^x−1)/x=

(c) Graph the function to see if it is consistent with your answers to parts (a) and (b). By graphing, find an interval for x near zero such that the difference between your conjectured limit and the value of the function is less than 0.01. In other words, find a window of height 0.02 such that the graph exits the sides of the window and not the top or bottom. What is the window?
______<=x<=______
_______<=y<=______