a) Approximate the change in $f(x, y)=\left(x^{2}+y^{2} ight) e^{x y}$ if $(x, y)$ changes from $(1,2)$ to $(0.98,2.01 $. (4 marks) b) If $z=e^{-t}\left(\sin \frac{x}{c}+\cos \frac{x}{c} ight), show that $\frac{\partial z}{\partial t}=c^{2} \frac{\partial^{2} z}{\partial x^{2}}$. (4 marks) c) Let $f(x, y, z)=x^{2}+y^{2}+z^{2}$, where $x= ho \sin \phi \cos \theta, y= ho \sin \phi \sin \theta$ and $z= ho \cos \phi$. Use chain rule to find $\frac{\partial f}{\partial ho} $ in terms of $ ho$. (4 marks) d) A box has length $x$, width $y$ and height $z$. Determine the dimensions of the box that will make the volume maximum if $4 x+3 y+z=12$. Show that the dimensions satisfies the loca. maximum properties based on second derivative test. (8 marks) CS. SD. 149