(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant 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] ]

3. 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

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# Homework Help: Taylor Polynomial Approximation of log(2.25)

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