# Calculus

Consider the function f(x)=(5^x−1)/x.

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.

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
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

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### Calculus

The function f is continuous on the interval [4, 15], with some of its values given in the table above. Estimate the average value of the function with a Right Rectangle Approximation, using the 4 intervals between those given

2. ### Algebra

This is the functions practice 1) which table of values does not represent a function? 2) given the function y=2x+3, what output values will result from the input values shown in the table? 3) which values for x and y will make

3. ### math help!!!

stuck!! pls help/explain!!! 2. Do the values in the table represent a linear function? If so, what is the function rule? (1 point) x = -2, 0, 2, 4 y = -4, 0, 4, 8 The values do not show a linear function. Yes, they show a linear

4. ### math

9. which set of output values correctly completes the function table? y=6-x input (X) output (y) -2 ? -1 ? 3 ? ----------------------- 4,5,3 -8,-7,3 8,7,3 11. What is the function rule shown by the table? input(x) output(y) -2 -3

1. ### Calculus

The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in the table below. Use the data in the table to approximate f '(3.5) x 3 4 7 10 13 f(x) 2 8 10 12 22

2. ### Math I need help ASAP!

1) Identify the function rule shown in the table. Function Table n - 3, 4, 5, 6 y - 2, 1, 0, -1 a. y = 2 + n b. y = 5n c. y = 5 - n d. not enough information ** 2) What is the values of the function y = -2x - 4 for x = 0,1,2 and

f is a function that is differentiable for all reals. The value of f ′(x) is given for several values of x in the table below. The table: x -8,-3,0,3,8 f'(x)-4,-2,0,4,5 If f ′(x) is always increasing, which statement about

4. ### Calculus

The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Trapezoidal Sum Approximation, using the intervals between those given points.

1. ### Calculus

1. The function is continuous on the interval [10, 20] with some of its values given in the table above. Estimate the average value of the function with a Left Hand Sum Approximation, using the intervals between those given

2. ### Statistics

Assume that a researcher randomly selects 14 newborn babies and count the number of girls, X. The probabilities corresponding to the 14 possible values of X are summarized in the given table. Answer the questions using the table.

3. ### Calculus

The function f is continuous on the interval [4, 15], with some of its values given in the table above. Estimate the average value of the function with a Trapezoidal Approximation, using the 4 intervals between those given points.