# Math Help - Estimate the Given Number

1. ## Estimate the Given Number

I'm having some trouble with the following problems.

Use a linear approximation (or differentials) to estimate the given number.

1. (8.06)^(2/3)
2. 1/1002

My book doesn't go over the process of how to do these problems. Thanks for any help.

2. Originally Posted by dm10
(8.06)^(2/3)
Let $f(x) = (8+x)^{2/3}$ then $f(h) \approx f(0) + hf'(0)$

Now $f'(x) = \tfrac{2}{3}(8+x)^{-1/3} \implies f'(0) = \tfrac{2}{3}\cdot 8^{-1/3} = \tfrac{1}{3}$

This means, $f(h) \approx 2 + \tfrac{h}{3}$

Now let $h=.06$

The other problem is similar.