Calculus
posted by Abi .
Consider the function f(x)=(4^x−1)/x.
(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<=______
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