# Linear Approximations

1. Oct 26, 2014

### _N3WTON_

1. The problem statement, all variables and given/known data
Use an appropriate linear approximation to estimate the value $(0.97)^{3}(2.02)$. Write your answer as a simplified decimal.

2. Relevant equations
Linearization:
$L(x,y) = f(a,b) + \frac{\partial z}{\partial x}(a,b)(x-a) + \frac{\partial z}{\partial y}(a,b)(y-b)$

3. The attempt at a solution
I am a little confused on this one about how to get going, but once I get started this shouldn't pose to much of a problem. I was thinking (I came here to confirm this thought) that I could define a function:
$z = x^{3}y$
Then I would take:
$a = 1 \hspace{2 mm} b = 2$
Then I would go from there and formulate the linearization. I just wanted to see if this was the right way to proceed or not..

Last edited: Oct 26, 2014
2. Oct 26, 2014

### Staff: Mentor

Looks like you're mostly on the right track, but your partials aren't right.

Since z = f(x, y), the partials you want are $\frac{\partial z}{\partial x}$ and $\frac{\partial z}{\partial y}$. It might be that you wrote them upside down inadvertently.

3. Oct 26, 2014

### Ray Vickson

Best policy: just go ahead and do it.

4. Oct 26, 2014

### _N3WTON_

Ah, thank you...I just wrote it down wrong by accident :)