6. The quadratic Taylor approximation of f(x, y) near (x, y) = (a, b) is given...

 

 

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6. The quadratic Taylor approximation of f(x, y) near (x, y) = (a, b) is given by fxx(a,b) f(x, y): Q(x, y) = f(a,b)+fx(a, b)(xa)+fy(a,b)(yb)+' -(x-a)+fxy (a, b)(xa)(yb)+ 2 2 fyy(a,b) (y-b) =e-x-y-xy Now consider f(x, y) (a) Find the linear approximation L(x, y) for f(x, y) at (0,0) (b) Find the quadratic Taylor approximation of f(x, y) at (0,0) (c) Graph f, L, and Q on one graph. You may want to use the GeoGebra 3D Plotter. Include the graph in your submission. 6. The quadratic Taylor approximation of f(x, y) near (x, y) = (a, b) is given by fxx(a,b) f(x, y): Q(x, y) = f(a,b)+fx(a, b)(xa)+fy(a,b)(yb)+' -(x-a)+fxy (a, b)(xa)(yb)+ 2 2 fyy(a,b) (y-b) =e-x-y-xy Now consider f(x, y) (a) Find the linear approximation L(x, y) for f(x, y) at (0,0) (b) Find the quadratic Taylor approximation of f(x, y) at (0,0) (c) Graph f, L, and Q on one graph. You may want to use the GeoGebra 3D Plotter. Include the graph in your submission.