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Calculus III - Practice Exam 1 Problems | MATH 237, Exams of Advanced Calculus

Material Type: Exam; Professor: Brown; Class: CALCULUS III; Subject: Mathematics; University: James Madison University; Term: Unknown 1989;

Typology: Exams

Pre 2010

Uploaded on 02/13/2009

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PRACTICE EXAM I
Math 237, Spring 2008
Answer each of the following problems as completely as you can. You must show
your work to receive credit. Progress in the right direction will be worth partial
credit.
THIS IS A PRACTICE EXAM. In particular, it is not an exhaustive list of topics
that are worth reviewing. The algebra of these problems, and typos generally, are
not vetted as carefully as they would be on a real test. It is also a little longer than
the real test will be.
(1) (a) What is the definition of (a,b)?
(b) How might one compute (a,b) for vectors in R3?
(c) Identify and sketch the surface: x2=3y2+4z2Label co-ordinate axes
and intercepts.
1
pf3
pf4
pf5

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PRACTICE EXAM I

Math 237, Spring 2008

Answer each of the following problems as completely as you can. You must show your work to receive credit. Progress in the right direction will be worth partial credit. THIS IS A PRACTICE EXAM. In particular, it is not an exhaustive list of topics that are worth reviewing. The algebra of these problems, and typos generally, are not vetted as carefully as they would be on a real test. It is also a little longer than the real test will be.

(1) (a) What is the definition of (a, b)?

(b) How might one compute (a, b) for vectors in R^3?

(c) Identify and sketch the surface: x^2 = 3y^2 + 4z^2 Label co-ordinate axes and intercepts.

1

(2) Suppose that a = 〈 2 , − 1 , 0 〉 and that b = 〈 4 , 3 , 7 〉.Compute each of the following: (a) compab

(b) The area of the parallelogram with sides a and b.

(c) The equation of the plane that contains both vectors and the point (13, 13 , 42).

(4) (a) Find the distance traveled along a circular helix centered around the z-axis from the point (1, 0 , 0) to the point (1, 0 , 4 π), if that corresponds to two complete revolutions.

(b) Give an arc length parametrization of this curve.

(5) Let P = (1, 0 , 2), Q = (− 2 , 1 , 2), and R = (0, − 1 , −1). Are P, Q, and R co-linear? If so, what is an equation of the line that contains them? If not, what is an equation for the plane that they determine?