Question

Use linearization to approximate (8.06)^2/3.

Answer 1

\[(8 + x)^{\frac{2}{3}} = 4(1 + \frac{x}{4})^\frac{2}{3}\]
\[(1 + \frac{x}{4})^\frac{2}{3} ≈ 1 + \frac{x}{6}\]
\[4(1 + \frac{x}{4})^\frac{2}{3} ≈ 4(1 + \frac{x}{6}) = 4 + \frac{2x}{3}\]
When x = 0.06,
(8.06)^(2/3) ≈ 4 + 2(0.06)/3 = 4.04

Answer 2

how did you get the first equation with the 4?

Answer 3

Because you factorize out the 8 from the bracket and then the 2/3 makes it a 4.