Download MA 166 Exam 1 Spring 1999: Vector Calculus and Integration and more Exams Analytical Geometry and Calculus in PDF only on Docsity!
MA 166 EXAM 1 Spring 1999 Page 1/
NAME
STUDENT ID
RECITATION INSTRUCTOR
RECITATION TIME
Page 1 /
Page 2 /
Page 3 /
Page 4 /
Page 5 /
TOTAL /
DIRECTIONS
- Write your name, student ID number, recitation instructor’s name and recitation time
in the space provided above. Also write your name at the top of pages 2, 3, 4 and 5.
- The test has five (5) pages, including this one.
- Write your answers in the boxes provided.
- You must show sufficient work to justify all answers. Correct answers with inconsistent
work may not be given credit.
- Credit for each problem is given in parentheses in the left hand margin.
- No books, notes or calculators may be used on this test.
(4) 1. Find a unit vector having the same direction as the vector ~a =
i +
j −
k.
(6) 2. If ~a = 2
i −
j + 2
k and
b =
i, find pr ~a
b.
(7) 3. Find the area of the triangle with vertices at (0, 0 , 0), (3, 2 , 0), and (2, 6 , 0).
(4) 4. Find x so that the vectors
~a =
i + 3
j − x
k and
b = (1 + x)
i +
j −
k
are perpendicular.
(8) 5. The points (1, 0 , 0) and (
7
3
2
3
2
3
) lie on a sphere with center at (a, −
1
3
1
3
) and
radius
- Find a.
(5) 6. A person pulls a sled 100 feet with a rope that makes an angle of
π
4
with the horizontal
ground. Find the work done on the sled if the tension in the rope is 5 pounds.
(24) 10. Evaluate the integrals:
(a)
x sin x dx
(b)
tan
2
x sec
4
x dx
(c)
cos
2
x sin
3
x dx
(d)
tan x sec
3
x dx
(18) 11. Evaluate the integrals. PARTIAL CREDIT will not be given unless steps are clearly
shown.
(a)
2
0
4 − x
2 dx
(b)
x
2
x
4
dx
