2. Consider the function f(x, y) = x 4y 3 . (a) Calculate the first-order Taylor

Question

2. Consider the function f(x, y) = x 4y 3 . (a) Calculate the first-order Taylor approximation to f(x, y) near the point (1,2) and use it to estimate the value of f(1.1, 2.2) (b) Calculate an upper bound on the error associated with this first-order approximation assuming that you only use values of x and y such that |x 1| 0.1 and |y 2| 0.2. (c) Now calculate the second-order Taylor approximation to f(x, y) near the point (1,2) and use it to estimate the value of f(1.1, 2.2) (d) Calculate an upper bound on the error associated with this second-order approximation, again assuming that you only use values of x and y such that |x 1| 0.1 and |y 2| 0.2.

Explanation / Answer

2. Consider the function f(x, y) = x 4y 3 . (a) Calculate the first-order Taylor

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