(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