Last Name: Name
Problem Session (Circle one):
Section 4 Section 5 Section 6
Math252Fall2011Geveci
Exam # 1 Type 1
1(14 pts.) Let
v=³3√2,−√2´,w=(4,2)
Make use of the dot product to determine the angle θ(in radians) between vand w(0≤θ≤π).
1
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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
1 / 6
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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).
- 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.
- 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).
- 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