Taylor Polynomial

forty

Using P₂(x,y), find a quadratic approximation to ln(1.25) to 4 decimal places.

The original function is f(x,y)=ln(x² + y²) and is about the point (1,0).

I calculated P₂ to be y²-x²+4x-3

however I don't know how to find a quadratic approximation. Do I just set say x=1 and y=.5?

Any help would be great!

Gib Z

Thats not exactly it, but on the right track. Just any values of x and y that make x^2 + y^2 = 1.25. (1, 0.5) would work, but would not give you 4dp accuracy. Something like (1.1, 0.2) would work somewhat better, but still nowhere near 4dp accuracy.

EDIT: I don't know how they expect you to get 4dp accuracy, seeing as even x^2=1.25 and y=0 gives only 2dp accuracy. Sorry