To approximate \( 15\sqrt{11} \) using the function \( g(x) = 15x \), we first need to calculate the value of \( \sqrt{11} \). The approximate value is \( \sqrt{11} \approx 3.3166 \). Therefore, we can compute \( 15\sqrt{11} \):
\[ 15\sqrt{11} \approx 15 \times 3.3166 \approx 49.749 \]
Now we need to find \( x \)-values where \( g(x) = 15x \) is close to \( 49.749 \). We can start with \( x = 3 \) (as given) and then find \( x \) values that can yield approximations of \( 15\sqrt{11} \).
To find suitable next values, we can increase \( x \) systematically. Let’s choose:
- \( x = 3 \)
- \( x = 3.1 \)
- \( x = 3.2 \)
- \( x = 3.3 \)
- \( x = 3.4 \)
- \( x = 3.5 \)
Now, we compute \( g(x) \) for these values:
- \( g(3) = 15(3) = 45 \)
- \( g(3.1) = 15(3.1) = 46.5 \)
- \( g(3.2) = 15(3.2) = 48 \)
- \( g(3.3) = 15(3.3) = 49.5 \)
- \( g(3.4) = 15(3.4) = 51 \)
The next five \( x \)-values that can be used to approximate \( 15\sqrt{11} \) starting with \( 3 \) are:
- \( 3.1 \)
- \( 3.2 \)
- \( 3.3 \)
- \( 3.4 \)
- \( 3.5 \)
These values will allow you to see how \( g(x) \) approaches \( 15\sqrt{11} \).
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