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March 29, 2015

March 29, 2015

Posted by **Sofia** on Thursday, September 20, 2012 at 11:43pm.

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.

- Calculus -
**Reiny**, Friday, September 21, 2012 at 9:10amI 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

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