Chapter 14.4, Problem 43E

To determine

(a)

Prove that $f\left(x,y\right)=L\left(x,y\right)+e\left(x,y\right)$.

To determine

(b)

Prove that $0\le \frac{e\left(x,y\right)}{\sqrt{{\left(x-2\right)}^2+{\left(y-1\right)}^2}}\le 4\left|y-1\right|$.

To determine

(c)

Prove that $f\left(x,y\right)$ is differentiable.