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Unformatted text preview: Spring 2007I M408D Test #2 McAdam
SHOW YOUR WORK
Points: 1) IO 2) 10 3) 10 4)10 5) 10 6) 10 7) 40
WRITE YOUR DISCUSSION SECTION TIME (or ESP) ON THE COVER 1) Name a nonzero 3-dimensional vectOr which is perpendicular to (1, 2, 1). (There are infinitely many of them. Give me any
one, except (0, 0, 0).) 2) Let 04 = (3, 2, 4) and [Z = (Z, 1, 2). Find a 3-dimensional unit
vector which is perpendicular to both o< and [3. *3) Find the equation of the plane containing the points
(2, 2, 2), (l, l, 0), and (1, 0, l).
4) MULTIPLE CHOICE: Which of the following five numbers is
& the distance from the point (I, 3, S) to the plane
2X + y + 22 + 9 = 0?
CHOOSE ONE: 0, 2, 4, 6, 8. (No work required.) 5) In the picture shown here, find the value of X which makes
the indicated length equal 2. 6) Here is a sketch of a parameteriZed curve 0(t) = (X(t), ylt)),
for O s t s 4. Make a sketch of X(t), for 0 s t g 4. (Make the scale on your sketch be about as big as on mine.) CAUTION:.~ My axes are the X-axis and the y-axis. What should
your axes be? 5M) X/AWI
7) Consider the parameterized curve 0(t) = (t2 - 1, 4/t). a) Sketch this curve for 1 < t g 3. Make one unit about as long as W, and show your scale.
b) To the sketch in part (a), add sketches of both
0"(2) and O’l/(Z). (Have those vectors start at 0(2).) c) Find the equation of the tangent line to the above curve at
the point 0(2). d) Set-up the integral you would use'to find the arclength of
this curve (for 1 s t s 3). Be explicit. Do not just give me the
general form, but rather apply it to this special case. DO NOT CALCULATE THE INTEGRAL. jUST SET IT UP. ...
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- Spring '07
- Multivariable Calculus