Question

Consider the function g(x)=15x Starting with 3, provide the next five x-values that can be used to approximate 15√11

Answer 1

To approximate \( 15\sqrt{11} \) using the function \( g(x) = 15x \), we can first find \( \sqrt{11} \). Since you started with \( x = 3 \), we can look at values around \( \sqrt{11} \).

We know that \( \sqrt{11} \) is approximately equal to \( 3.3166 \), so to approximate this with \( g(x) \), we will use x-values close to this number.

Starting from \( x = 3 \), let's adjust by adding a fraction of the difference to move towards \( \sqrt{11} \):

1. First value: \( x_1 = 3.1 \)
2. Second value: \( x_2 = 3.2 \)
3. Third value: \( x_3 = 3.3 \)
4. Fourth value: \( x_4 = 3.4 \)
5. Fifth value: \( x_5 = 3.5 \)

The next five \( x \)-values that we can use to approximate \( 15\sqrt{11} \) are:

1. \( 3.1 \)
2. \( 3.2 \)
3. \( 3.3 \)
4. \( 3.4 \)
5. \( 3.5 \)

Using these \( x \)-values in the function \( g(x) = 15x \) will yield approximations for \( 15\sqrt{11} \).