In-class work for 21 June 2012
1.) Find the linearization $L(x,y)$ of the function...
    a.) $f(x,y) = \sqrt{25-x-13y^2}$ at the point $(3,1)$.
    b.) $f(x,y) = \cos(xy)$ at the point $(\sqrt{\pi},\frac{\sqrt{\pi}}{2})$
    c.) $f(x,y) = \sqrt[3]{xy^2+y}$ at the point $(1,1)$.

2.) Find the differential of the function...
    a.) $z=cos(x)\log(y^2)$
    b.) $T = \frac{wx}{wx+yw^2}$
    c.) $v = z \sin(yx)$
    d.) $R = 2x \log(z) y$

3.) The dimensions of a close rectangular box are measured as $80 cm, 60 cm,$ and $50 cm$ respectively, which an error in measurement of at most $0.1 cm$ in each. Use differentials to e stimate the maximum error in the calculated area of the rectangle.

4.) If $x=u^2v, y=u+v, z=xy^3$, compute $\frac{\partial z}{\partial u}$ and $\frac{\partial z}{\partial v}$ when $u=1$ and $v=2$.

5.) If $M=xe^{y-z^2}$, $x=2u+v$, $y=\log(v-u)$, $z=v-2u$, then compute $\frac{\partial M}{\partial u}$ and $\frac{\partial M}{\partial v}$ when $u=1$ and $v=2$.