Question 4

a. If $xyz - u = 0$, $x^2 + y^2 + z^2 - v = 0$, and $x + y + z - w = 0$, find $\dfrac{\partial(x,y,z)}{\partial(u,v,w)}$. (2 marks)

b. Obtain a quadratic Taylor's series approximation to the function $f(x,y) = \cos x\cos y$ about the point $(0,0)$. Also, estimate the maximum absolute error in the region $|x| < 0.2$, $|y| < 0.1$. (3 marks)