Let f(x, y) = exp(3x + 2xy). (a) If h, k are small increments in x,...

Transcribed Image Text:

Let f(x, y) = exp(3x² + 2xy). (a) If h, k are small increments in x, y, respectively, obtain the first six terms in the Taylor series expansion of the function f about the point (1,1). (19 marks) (b) Show further that the following identity holds for f: f.-3f, + f, +(f, /x) - 12xf = 2yf. Let f(x, y) = exp(3x² + 2xy). (a) If h, k are small increments in x, y, respectively, obtain the first six terms in the Taylor series expansion of the function f about the point (1,1). (19 marks) (b) Show further that the following identity holds for f: f.-3f, + f, +(f, /x) - 12xf = 2yf.