Posted by **Abi** on Wednesday, February 9, 2011 at 10:48pm.

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<=______

## Answer this Question

## Related Questions

- Calculus - Consider the function f(x)=(4^x−1)/x. (a) Fill in the ...
- Calculus - Consider the function f(x)=sin(5x)/x. (a) Fill in the following table...
- Calculus - (a) By graphing the function f(x) = (cos 2x − cos x)/x2 and ...
- Calculus - (a) By graphing the function f(x) = (cos 2x − cos x)/x2 and ...
- Calculus - Consider the function f(x)=(5^x−1)/x. A) Fill in the table ...
- Calculus - For each value of h, evaluate the following function. Round your ...
- Calculus - For each value of h, evaluate the following function. Round your ...
- Calculus - Calculate the average rate of change of the given function f over ...
- Calculus - Compute the average velocity over time intervals [4, 4.01] , [4, 4....
- Math - The point P(8, −3) lies on the curve y = 3/(7 − x). (a) If Q ...