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Calculus III - Exam 1 Questions | MATH 252, Exams of Mathematics

Material Type: Exam; Professor: Geveci; Class: CALCULUS III; Subject: Mathematics; University: San Diego State University; Term: Fall 2011;

Typology: Exams

2010/2011

Uploaded on 11/17/2011

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Last Name: Name
Problem Session (Circle one):
Section 4 Section 5 Section 6
Math252Fall2011Geveci
Exam # 1 Type 1
1(14 pts.) Let
v=³32,2´,w=(4,2)
Make use of the dot product to determine the angle θ(in radians) between vand w(0θπ).
1
pf3
pf4
pf5

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Last Name: Name Problem Session (Circle one): Section 4 Section 5 Section 6

Math 252 Fall 2011 Geveci Exam # 1 Type 1

1 (14 pts.) Let v =

, w = (4, 2)

Make use of the dot product to determine the angle θ (in radians) between v and w ( 0 ≤ θ ≤ π).

  1. Let v = 3i + 2j and w = 3i − j. a) (4 pts) Determine the normalization of w (the unit vector along w).

b) (12 pts.) Determine P (^) wv, the projection of v onto w.

  1. Assume that the position of a particle at time t is

σ (t) = (cos (2t) , − sin (3t))

and C is the curve that is parametrized by σ (t). a) ( 8 pts.) Determine the velocity and acceleration of the particle at time t.

b) ( 10 pts.) Determine a vector-valued function L = (x (u) , y (u)) that parametrizes the tangent line to C at σ (π/6).

  1. Determine the indicated derivative: a) (4 pts.) ∂ ∂x exp^

¡x (^4) − y 3 ¢

(exp (u) = eu).

b) (4 pts.) ∂ ∂y ln

³p x^3 + y^4

c) (4 pts.) ∂ ∂z

Ã

(x^2 − y^2 − z^2 )^1 /^2