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Math203, Demo Exam #1 (Chapters 12-14)
Directions: Answer all of the questions. The problems will have their weights assigned next
to them. Show all work for maximal credit. No notes, cellular phones, pagers, calculators,
books or friends. Good luck.
1) Definitions.
a. What is a Vector? What does it represent? Provide an example.
b. What does the Dot Product signify? Provide an example.
c. For a single variable function f(x), what does it mean when we state that )(lim
3
xf
x→
exists?
d. For the multivariable function f(x,y), what does it mean when we state that
),(lim
2,3
yxf
yx →→
exists?
e. What do contour lines represent?
f. Define the directional derivative and provide an example.
2) For the function, ( ) ( )22 3541 ++−= yxz , perform the following. Be sure to explain
your reasoning.
a. Draw the function on the x-y plane as a set of contours representing static values of
z.
b. Draw the function on the y-z plan as a set of contours repre...

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