MAT397-2007Spring

# MAT397-2007Spring - V9CCHoTff FINAL MAT397 SPRING 2007 I....

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V9CCHoTff FINAL MAT397 SPRING 2007 I. (8 points) Find the vector projection, projab, of b onto a when a = 2i - 3j + k and b = i + 6j - 2k. 2. (8 points) Find an equation of the plane through the point (1,6, -5) and parallel to the plane x + 2y + 3z + 7 = O. Date: April 23, 2007.

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FINAL MAT:197 SPRING 2007 3. (8 points) Find the time t and the point (x(t),y(t), z(t)) on the curve x = t 2 -l,y = t 2 + 1, z = t + 1 at which the tangent line to this curve is parallel to the vector i + j + k. 4. (8 points) A moving particle has initial velocity v(O) = (1,1, -1). Its acceleration is a( t) = (2t, 3t 2 , sin t). Find its velocity at time t.
FINAL MAT397 SPRING 2007 4 5. (16 points) Find all the critical points of the function f(x, y) = x - 4xy + y4 + 4. For each critical point, use the second derivative test to decide whether it is a local maximum, local minimum or a saddle.

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4 FINAL MAT397 SPRING 2007

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## This note was uploaded on 06/16/2011 for the course MATH 397 taught by Professor Na during the Spring '11 term at University of North Carolina School of the Arts.

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MAT397-2007Spring - V9CCHoTff FINAL MAT397 SPRING 2007 I....

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