Use the function f(x)=3x to find the approximation 33√, correct to three decimal places, by creating a table with x-values closer and closer to 3–√ and the corresponding f(x) values.

Answer 1

To approximate 33√ using the function f(x) = 3x, we need to find the x-value that corresponds to the value 3–√. We will create a table with x-values closer to 3–√ and the corresponding f(x) values.

Let's start with x = 1:
f(1) = 3(1) = 3

Next, let's try x = 1.1:
f(1.1) = 3(1.1) ≈ 3.3

Then, let's try x = 1.01:
f(1.01) = 3(1.01) ≈ 3.03

Next, let's try x = 1.001:
f(1.001) = 3(1.001) ≈ 3.003

Continuing this pattern, we can calculate f(x) for x-values closer and closer to 3–√. We can see that as x gets closer to 3–√, the corresponding f(x) values approach the value of 33√.

Therefore, 33√ ≈ 3.003, correct to three decimal places.