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!