Hey guys
I am having a few issues with my linear algebra course. Me and my friends are in a study group and we are working on this problem for one of our seminars:
3. Find the linear and quadratic approximations to the funtion f(x,y)=e^(ax-by) around the point (0,0)
We think we have found the linear approximation of this as:
1 + xae^(ax-by) - ybe^(ax-by)
Is this correct? How do we get the quadratic approximation?
Hope you can help guys, it would be much appreciated.
Thanks for the help guys! it is much appreciated. So following that for the quadratic you get the formula below when evaluated at (0,0), correct?
The reason I ask is because the way this material was presented in lectures was in vector/matrices form and following that method my answer is subtly different due to as it becomes
due to a term.
You may have misunderstood that "1/2". If you have the quadratic form , you can write that as the matrix multiplication
.
Note that the "1/2" is only in the off diagonal terms. It is there so that when you multiply that out and add the two "xy" terms, it sums to bxy.
yeh apologies I meant to change my answer to:
So I understand how it comes to bxy in your example. But do not understand why the 1/2 is only in the off diagonal terms; because all the examples I am able to find online seem to have 1/2 for all terms? Thanks again for your help.