Consider a function of two variables, f(x, y). State the Taylor series expansion for f(x +...

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Consider a function of two variables, f(x, y). State the Taylor series expansion for f(x + Ax, y + Ay) about the point (x, y) up to second order. [2 marks] (b) Using the Taylor expansion of a function of one variable f(z) show that f(x+ Ar)-f(x-Ar) 2AT and df dr d²ff(x+Ax) + f(x– Ax) — 2f (x) - AT² I dr² (c) Consider the following function of two variables: f(x, y) = e-(+2y+v²) [4 marks] Use the Taylor expansion correct to first order to estimate f(0.2, 0.1), based on the fact that f(0,0) = 1. [4 marks] Consider a function of two variables, f(x, y). State the Taylor series expansion for f(x + Ax, y + Ay) about the point (x, y) up to second order. [2 marks] (b) Using the Taylor expansion of a function of one variable f(z) show that f(x+ Ar)-f(x-Ar) 2AT and df dr d²ff(x+Ax) + f(x– Ax) — 2f (x) - AT² I dr² (c) Consider the following function of two variables: f(x, y) = e-(+2y+v²) [4 marks] Use the Taylor expansion correct to first order to estimate f(0.2, 0.1), based on the fact that f(0,0) = 1. [4 marks]

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a The Taylor series expansion for fxx yy about the point xy up to second order is fxx yy ... View the full answer