Linear Approximation of 1/(5+x)^1/2

[Fiorella]

Homework Statement

Here is a picture of the problem: http://i3.photobucket.com/albums/y62/Phio/34.jpg" [Broken]

Homework Equations

y - f(c) = f '(c) (x - c)

The Attempt at a Solution

1/(5+x)^1/2 = (5 + x) ^ -1/2 = (1/5)^(1/2) * (1 + x/5)^(-1/2)

I have this. But I don't know if I'm on the right track...

 

[HallsofIvy]

I don't know what you are doing! You have rewritten the formula in a couple of different ways but you seem to have made no attempt to find either f'(c) or f(c), which you need to use "y- f(c)= f'(c)(x- c)".

 

[tiny-tim]

Hi Fiorella!

(try using the X² tag just above the Reply box )

1/(5+x)^1/2 = (5 + x) ^ -1/2 = (1/5)^(1/2) * (1 + x/5)^(-1/2)

I have this. But I don't know if I'm on the right track...

(I've no idea why you think "y - f(c) = f '(c) (x - c)" is relevant … but anyway:)

The answers given are clearly wrong …

at x = 0, f(x) = 1/√5, which does not match.

But your method is correct …

just carry on regardless! ​