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....
Hello, math34!
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!