# Estimating Using Differentials

• Apr 15th 2009, 02:31 PM
Afterme
Estimating Using Differentials
I'm trying to understand this concept but the teacher kind of made it unclear.

The problem is

a. Sqrt(108)
b. Sqrt(1002)

For a. what the teacher did was:

a = 100 x = 8
F(x) = sqrt(x) F'(x) = 1/2sqrt(x)

Am I supposed to use the Linearlization formula to estimate this? Also why is a = 100 and x = 8?
• Apr 15th 2009, 03:46 PM
Jhevon
Quote:

Originally Posted by Afterme
I'm trying to understand this concept but the teacher kind of made it unclear.

The problem is

a. Sqrt(108)
b. Sqrt(1002)

For a. what the teacher did was:

a = 100 x = 8
F(x) = sqrt(x) F'(x) = 1/2sqrt(x)

Am I supposed to use the Linearlization formula to estimate this? Also why is a = 100 and x = 8?

if your formula is $\displaystyle f(x) \approx f(a) + f'(a)(x - a)$, then you use $\displaystyle x = 108$ and $\displaystyle a = 100$ (where $\displaystyle f(x) = \sqrt{x}$)

that's using linear approximation. very close (indeed, equivalent) to using differentials, it should be acceptable

(by what you wrote, i am sure your professor said a = 100 and dx = 8)