1. (10 points) For each function given, 0 Draw and label a level curves diagram (contour map) of the function. Please label the axes and at least three contours. 0 Describe the graph of the function in a few words and draw a rough sketch of the function. (a) ay) = 1 +9m2 +312 (b) f(a=1y)= 52r-y 2. (15 points) Consider the future value of an investment of $1000 after t years in an account with continuous compounding at a nominal annual interest rate of 7' (as a decimal). This is F(t,r) = 10006" dollars . (a) Compute Interpret your answer in words, using units. eel 6r (10,0.072)' (b) Compute Interpret your answer in words, using units. E' at (10,0.072)' (c) Explain how the rate of change in (a) is related to a graph of a cross-sectional (trace) function of F(t, 1"). Sketch the graph in the appropriate two-dimensional plane. 3. (12 points) Does this make sense? Each of the following statements is mathematically incorrect. Write down why each statement is wrong, pointing out one or more specic flaws in the reasoning or notation. Then, rewrite the statement in a way so as to make it mathematically correct. (a) f(:r, y) = a: is a line that passes through the origin. ( b) Let f(:c, y) = scln(a: +y). Then, fl = . (e) Let g(a:,y) = $2 + scy2. Then 935 = 2:5 +y2 and 9W 2 2. (d) Let Mm, y) = ln(m) + e" sin(y). Then hy = ln(:c) + 6x cos(y)