The first six terms of the Taylor series of a function f (x,y) about the general...

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The first six terms of the Taylor series of a function f (x,y) about the general point (x, y) are S(x + h, y+k) = f + hf, + kf, +Ih'f + 2hkf, + k° f„]+•, where h,k are respective (small) increments in x,y. (a) Show that the corresponding series for the function f(x,y)= sin(x)/y about the point x = Tt/2, y=1 (with the same respective increments), is + h,1+ k =1-k- +* (19 marks) (b) Hence, or otherwise, use these terms in the series to estimate f(1ln/20,1.1) [3 marks], and compare your approximate answer with the exact value showing [3 marks] that the difference is 2.35 x10 (approximately). The first six terms of the Taylor series of a function f (x,y) about the general point (x, y) are S(x + h, y+k) = f + hf, + kf, +Ih'f + 2hkf, + k° f„]+•, where h,k are respective (small) increments in x,y. (a) Show that the corresponding series for the function f(x,y)= sin(x)/y about the point x = Tt/2, y=1 (with the same respective increments), is + h,1+ k =1-k- +* (19 marks) (b) Hence, or otherwise, use these terms in the series to estimate f(1ln/20,1.1) [3 marks], and compare your approximate answer with the exact value showing [3 marks] that the difference is 2.35 x10 (approximately).