Sample Calculus Quiz
LaTex2HTML Version
Problem #1
The following table gives the windchill W (° F)
at various temperatures T (° F) and wind speeds
v (mph).
Windchill Factor
|
T = 15 |
T = 10 |
T = 5 |
T = 0 |
| v = 15 |
-11 |
-18 |
-25 |
-31 |
| v = 20 |
-17 |
-24 |
-31 |
-39 |
| v = 25 |
-22 |
-29 |
-36 |
-44 |
- Use the table to find approximate values for
,
when T=0 and v=25.
- Using the table and your answers to 1), give (an approximation of) the
local linearization for W
around T=0 and v=25.
- Use the local linearization to approximate W when T=-5 and
v=25.
Problem #2
Suppose you are given two infinite
wires which are parallel to the z-axis, passing through the points
and 
in the xy
plane which are homogeneously and
oppositely charged.
The potenial energy P of a unit charge in the xy plane
is given by
- What is the gradient of the potential energy at
?
- What is the rate of change of P in the direction
at 
?
- An equipotential line is a curve along which the electrical
potential is constant. What is the direction of the equipotential line
passing through
?
- Another particle with a unit charge is moving up the y axis at a rate
of
. What is the rate of change of the potential energy of this
particle?
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Created: January 10, 1997
Comments to:
alexsuciu@neu.edu
http://www.math.neu.edu/~suciu/quiz/lt2/latex2htmlquiz.html