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MA 261 Exam 1 Spring 2000 Page 1/
NAME
STUDENT ID
RECITATION INSTRUCTOR
RECITATION TIME
DIRECTIONS
- Fill in the above information. Also write your name at the top of each page of the
exam.
The test has 9 pages, including this one.
Problems 1 through 6 are multiple choice; circle the correct answer.
Problems 7 through 10 are problems to be worked out. Write your answer in the
box provided. YOU MUST SHOW SUFFICIENT WORK TO JUSTIFY YOUR
ANSWERS. CORRECT ANSWERS WITH INCONSISTENT WORK MAY NOT
RECEIVE CREDIT.
Points for each problem are given in parenthesis in the left margin.
No books, notes, or calculators may be used on this test.
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(10) 1) Parametric equations for the line that contains the point (1, โ 2 , 3) and is perpendicular
to the plane 3x โ 4 y + 2z = 8 are:
A. x = 1 + 3t, y = โ 2 โ 4 t, z = 3 + 2t
B. x = 3 + t, y = โ4 + 2t, z = 2 + 3t
C. x = 8 + 3t, y = 8 โ 4 t, z = 8 + 2t
D. x = โ1 + 3t, y = 2 โ 4 t, z = โ3 + 2t
E. x = โ 1 โ 3 t, y = 2 + 4t, z = โ 3 โ 2 t
(10) 2) lim
(x,y)โ(0,0)
sin(x
2
2
)
(x
2
2 )
ยท (y + 2) is equal to:
A. 0
B. 1
C. 2
D. 4
E. Does not exist.
- An object has acceleration
โโ
a(t) = e
t ~ i+
k, initial velocity
โโ
v(0) =
i, and initial position
โโ
r(0) = 2
j. Find the position vector of the object at time t = 1.
A. (e โ 1)
i โ 2
j +
k
B. (e โ 1)
i + 2
j +
k
C. e~i โ 2
j
D. e~i + 2
j +
k
E. e~i + 2
j โ
k
(10) 6) Let f (x, y) = ln(x
2
2 ) with x = g(t) and y = h(t). Assuming that g(0) = 1,
h(0) = 3, g
โฒ
(0) = 2, and h
โฒ
(0) = 4, the value of
d
dt
(f (g(t), h(t)) when t = 0 is:
A.
B.
C.
D.
E.
- Consider the curve given by:
โโ
r(t) = t
2 ~ i + 2t~j + (ln t)
k, 1 โค t โค e.
(6) a) Write down an integral that gives the arclength L of this curve (including limits
of integration).
Answer to 8.a) L =
(4) b) Compute the integral in 8.a) to get the exact value of the arclength L.
Answer to 8.b) L =
- Let f (x, y) = x
2 e
xy .
(6) a) Find
2 f
โxโy
Answer to 9.a)
2 f
โxโy
(4) b) What is
2
f
โxโy
at the point (1, 0)?
Answer to 9.b)
2
f
โxโy
