Consider the function f(x)=(5^x−1)/x.

Question

A) Fill in the table values for f(x):
x= -0.1, -0.01, -0.001, -0.0001, 0.0001, 0.001, 0.01, 0.1
f(x)= 1.4866, 1.5866, 1.6081, 1.6093, 1.6096, 1.6107, 1.6225, 1.7462
B) Based on the table values, what would you expect the limit of f(x) as x approaches 0 to be?

lim (5^x-1)/x= 1.60
x--->0

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 <_ _________

So far, everything I've done is correct for a and b. The online program we use for turning in homework allows us to preview the correctness of our answers. My issue is finding part C. When I use -0.02 and 0.02 for the x-range, I cannot find y. I've tried the epsilon-delta scheme, but I'm having trouble understanding that. I'm in a pinch on this homework question.

Answer 1

I assume you used a calculator to find f(x) for the given values of x
Why are you having difficulty finding f(-.02) and f(.02) ?

my calculator gives me
f(-.02) = 1.5836..
f(.-2) = 1.6356..

so

-.02 ≤ x ≤ .02
1.5836 ≤ y ≤ 1.6356