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Unformatted text preview: Math 20C Final Exam 90 points March 19, 2008 • Print Name and ID number on your blue book. • BOOKS and CALCULATORS are NOT allowed. Two pages of NOTES (both sides) are allowed. • You must show your work to receive credit. 1. (10 pts.) The vertices of a triangle are O (0 , , 0), A (0 , 1 , 1) and B (1 , , 3). (a) Compute the area of the triangle. (b) Compute the size of angle AOB . You may leave trig functions in your answer. 2. (8 pts.) Find the equation of the plane passing through (1 , , 1) and containing the line with symmetric equations x = 2 y = 3 z . 3. (8 pts.) Find the unit tangent vector to r ( t ) = 4 √ t i + t 2 j + t k at t = 1. 4. (8 pts.) Your are given that z = f ( x,y ), x = u + v and y = u 2 v . Use the chain rule to compute the following. (a) z u = ∂z/∂u (b) z uv = ∂ 2 z/∂u∂v. Of course, you will have to leave expressions such as f x ,f xy and so on in your answer since the partial derivatives of f are not known....
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This note was uploaded on 08/14/2011 for the course MATH 20 C taught by Professor Ronevans during the Spring '08 term at UCSD.
 Spring '08
 RONEVANS
 Math, Multivariable Calculus

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