Estimate the Given Number

**dm10** · October 26th 2008, 07:36 AM

I'm having some trouble with the following problems.

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

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

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

**ThePerfectHacker** · October 26th 2008, 08:04 AM

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.

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