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.
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.
Let $\displaystyle f(x) = (8+x)^{2/3}$ then $\displaystyle f(h) \approx f(0) + hf'(0)$
Now $\displaystyle f'(x) = \tfrac{2}{3}(8+x)^{-1/3} \implies f'(0) = \tfrac{2}{3}\cdot 8^{-1/3} = \tfrac{1}{3}$
This means, $\displaystyle f(h) \approx 2 + \tfrac{h}{3}$
Now let $\displaystyle h=.06$
The other problem is similar.