Use differentials to approximate the value of 7.8^3??

Should be easy, but canīt find the correct answer. How do you do this... help....

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- Nov 30th 2006, 07:57 AMmath34Use differentials to approximate?
Use differentials to approximate the value of 7.8^3??

Should be easy, but canīt find the correct answer. How do you do this... help.... - Nov 30th 2006, 08:26 AMSoroban
Hello, math34!

Quote:

Use differentials to approximate the value of

Evidently, we have the function: .

Then: .

We know that: .

Let

Then: .

Hence: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

How good is this approximation?

The actual value is: .

Our answer is short by only: .

As a percent: .

We were off by only two-tenths of a percent (2 parts in 1000) . . . not bad!

- Nov 30th 2006, 08:30 AMCaptainBlack
- Nov 30th 2006, 09:02 AMmath34How did you get -0.2 for dx?
Thanks

- Nov 30th 2006, 09:13 AMmath34How did you get -0.2 for dx? ,,
- Nov 30th 2006, 09:29 AMThePerfectHacker
Because that was the decrease in the value. You went from 8 to 7.8 thus the change was -.2