\item  
Section 3.5: % Derivatives of Trigonometric Functions
problems 17, 49, 57, 58.

% Homework assignments for week 4

\item  
Section 3.6: % The Chain Rule
Do as many as time permits from problems 51, 53, $\cdots$, 75.

\item  
Assume $g(2)=3$, $g'(2)=0.1$, $f'(2)=3$, $f'(3)=4$ and $f'(4)=5$.
What is ${d \over dx} f(g(x))$ at $x =2$?

\item  
Section 3.7: % Implicit Differentiation
problems 27, 31, 42, 48. % problem 48 = d/dx x^(q/p)

asec 
Start with domain and range for $\csc$ and $\csc^{-1}$,
derive the formula for the derivative of $\csc^{-1}$.
e component test.
\item
The natural domain for both $\vF$ and
$\vG$ is $\{(x,y,z), \, x^2+y^2 \neq 0 \}$
(that is where $\vF$ and $\vG$ are defined).
Show that $\vF$ is conservative in this domain by finding
its potential function.
\item
Show that $\vG$ is NOT conservative in this domain (read example 5).
\item
If given another $\vH$ satisfying the component test in this
domain, how do you determine whether $\vH$ is conservative?
\end{enumerate}

\item
Let $\vF = { x \over \sqrt{x^2+y^2+z^2}} \vi +
         + { y \over \sqrt{x^2+y^2+z^2}} \vj +
         + { z \over \sqrt{x^2+y^2+z^2}} \vk$.
What is the natural domain for $\vF$? 
Show that $\vF$ satisfies the component test in this domain.
Is this domain simply connected?
Is $\vF$ conservative in this domain? 

% 16.4: Green's Theorem in the Plane.
\item
Section 16.4: Problems 10, 17, 19, 23, 27, 29, 38, 39.

% 16.5: Surface and Area.
\item
Section 16.5: 5, 6, 11, 13, 15, 19, 23, 25, 31, 33, 45, 49, 51, 55, 56. 

% 16.6: Surface Integrals.
\item
Section 16.6: Problems 17, 19, 21, 25, 35, 37.

% 16.7: Stokes's Theorem.
% 16.8: The Divergence Theorem and a Unified Theory.