To approximate \( \sqrt[3]{1511} \) using the function \( g(x) = 15x \), we can identify a reasonable starting point and determine the next five values of \( x \) that will lead us toward approximating the cube root.
The cube root of a number \( a \) can be approximated using the function \( g(x) = ax \) to find a value of \( x \) such that \( g(x) \) is approximately equal to the number you want to find the cube root of.
Starting with \( x = 3 \):
- Next x-value: We can make an educated guess for the subsequent values by increasing them slightly. Let's say \( x = 3 + 1 = 4 \).
- Next x-values: Then we'll add 1 again, leading to \( 5, 6, 7, \) and \( 8 \).
Here we go:
- \( 3 \)
- \( 4 \)
- \( 5 \)
- \( 6 \)
- \( 7 \)
- \( 8 \)
So the sequence becomes:
3, 4, 5, 6, 7, 8.
In conclusion, starting from 3, the next five \( x \)-values that can be used to approximate \( \sqrt[3]{1511} \) are \( 4, 5, 6, 7, \) and \( 8 \).
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