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## Homework Statement

Determine the order two Taylor polynomial, p

_{2}(x, y), for

f(x, y) = log

_{e}(1 + x

^{2}+ y

^{4})

about point (0, 1)

**ANSWER:**

log

_{e}(2) + 2y - 2 + [tex]\frac{1}{2}[/tex] [ x

^{2}- 2y

^{2}+ 4y - 2 ]

Managed that question and should be correct. If not, do let me know =)

__Part 2: Using p___{2}(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

**p**

_{2}(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 p

_{2}(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