State and prove Taylor's theorem for f(x,y)



State and prove Taylor's theorem for f(x,y)..

Answer / Amit Kumar Bhaskar

Taylor's Theorem for functions of two variables states that if f(x,y) is a function with continuous partial derivatives up to order n+1 in an open disk D containing the point (a,b), then there exists a point (c,d) between (a,b) and the point z=(x,y) such that f(x,y) can be expressed as a sum of Taylor polynomial plus a remainder term.

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