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5.

(a) Let f(x, y) be a function of two variables, and (xo, yo) be the coordinates of a point in the

Oxy plane. Write down the Taylor series expansion for f about the point (ro, yo) up to and

including terms of degree two.

[2 marks]

(b) Find the second order Taylor expansion of f(x, y) = √/1+4x² + y² about (xo, Yo) =

(1, 2)?

[4 marks]

(c) Use your result to compute f(1.1, 2.05) approximately. How does it compare with the value

calculated directly from f(x,y)?

[1 marks]

(d) Find the second order Taylor expansion of f(x, y) = e²¹ sin(3y) about (xo, Yo) = (0,0)?

[3 marks]

[Total: 10 marks]

Fig: 1