What were you like when you were younger? Think of several words that describe you. Then, use them in sentences about yourself. One has been done for you.

$$\begin{array}{|l|l|} \hline \text { Palabras descriptivas } & \text { Oración sobre mí } \\ \hline \text {generoso(a)} & \begin{array}{l} \text {Era muy generoso(a)} \text { con mis } \\ \text {hermanos pequeños.} \end{array} \\ \hline & \text{Era} \\ \hline & \text{Era}\\ \hline & \text{Era} \\ \hline \end{array}$$

Find the residues of the following functions at the indicated points. Try to select the easiest of the methods outlined above. Check your results by computer. $\frac{1-\cos 2 z}{z^{3}} \text { at } z=0$

Set of functions is linearly independent if their Wronskian is not identically zero. Calculate the Wronskian of each of the following sets to show that in each case they are linearly independent. For each set, write the differential equation of which they are solutions. Also note that each set of functions is a set of basis functions for a linear vector space and that the general solution of the differential equation gives all vectors of the vector space. $\sin \beta x, \cos \beta x$

Identify a convergence test for each of the following series. If necessary, explain how to simplify or rewrite the series before applying the convergence test. You do not need to carry out the convergence test. $\sum_{k=10}^{=} \frac{100^{k}}{k ! k^{2}}$

Show that $\int_{0}^{2} \int_{0}^{2}(1-y) d x d y=0$. Does the double integral represent the volume of a solid? Explain.

Medicine. The body temperature (in degrees Fahrenheit) of a patient t hours after taking a fever-reducing drug is given by $F(t)=0.16 t^{2}-1.6 t+102$. Find F(4) and $F^{\prime}(4)$. Write a brief verbal interpretation of these quantities.

Find the future value of each annuity. There are payments of $1500 at the end of each year for 6 yr at 0.5% interest compounded annually.

Graph the region R bounded by the graphs of the equations. Use set notation and double inequalities to describe Ra s a regular x region and a regular y region, whichever is simpler. $y=x^{2}, y=9,0 \leq x \leq 3$

Evaluate each of the following in $x + iy$ form, and compare with a computer solution. $2^i$

You are playing the fortune-teller at your school's winter carnival. Some of your friends want to find out what is going to happen to them in the future. Write at least three predictions for each of the people listed below. The first one has been started for you. Nombre de un(a) amigo(a) _____ Predicciones: Mi amigo tendrá una casa grande.

The graph at right gives information about three new tile patterns. Remember that in this course, tile patterns will be considered to be elements of continuous relationships and thus will be graphed with a continuous line or curve. a. What information does the circled point on the graph tell you about tile pattern A? b. Find the growth of each tile pattern. For example, how much does tile pattern A increase from one figure to the next? Explain how you know. c. Look at the lines for tile patterns A and B. What is the same about the two lines? What conclusion can you make about these tile patterns? What is different about the lines? What does this tell you about the tile patterns? Use what you see on the graph to justify your answers. d. Look at lines A and C on the graph. What do these two lines have in common? In what ways are the lines different? What does this tell you about the tile patterns? Explain completely.

For each of the following differential equations, separate variables and find a solution containing one arbitrary constant. Then find the value of the constant to give a particular solution satisfying the given boundary condition. Computer plot a slope field and some of the solution curves. $\left(1+y^{2}\right) d x+x y d y=0$, y = 0 when x = 5.

Explain how to subtract two matrices.

$$\left[\begin{array}{lll} 10 & -4 & 6 \end{array}\right]-\left[\begin{array}{lll} -2 & 5 & 3 \end{array}\right]$$

Use vectors, and also the dot and cross product, to prove the following theorems from geometry. The median to the base of an isosceles triangle is perpendicular to the base.