- #1
RyanV
- 12
- 0
Homework Statement
Determine the order two Taylor polynomial, p2(x, y), for
f(x, y) = log e (1 + x2 + y4)
about point (0, 1)
ANSWER:
loge (2) + 2y - 2 + [tex]\frac{1}{2}[/tex] [ x2 - 2y2 + 4y - 2 ]
Managed that question and should be correct. If not, do let me know =)
Part 2: Using p2 (x, y), find a quadratic approximation to log e (2.25) to 4 decimal places. Use a calculator to find the value of log e (2.25) to 4 decimal places, and comment on your answer.
Homework Equations
2nd Order Taylor Polynomial
p2(x, y) = f(x, y) + (x + a)[tex]\frac{\partial f}{\partial x}[/tex] + (y + b)[tex]\frac{\partial f}{\partial y}[/tex] + [tex]\frac{1}{2}[/tex] [ (x - a)2[tex]\frac{\partial ^2 f}{\partial x^2}[/tex] + (x - a)(y - b)[tex]\frac{\partial ^2 f}{\partial x\partial y}[/tex] + (y - b)2[tex]\frac{\partial ^2 f}{\partial y ^2}[/tex] ]
The Attempt at a Solution
I'm not too sure where to go from there...I thought of putting p2(x, y) as log 2 (2.25) but I'm not sure what that does after simplifying...
Any assistance would be of much help! =)
Thanks