hw13 e3practice

# hw13 e3practice - -∞< t< ∞ b Find the velocity...

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15.7 p 966 31, 35 15.8 p 976 3, 5, 7, 9, 15, 17, 25, 40, 41 H w 13 T his W eek e xam iii Covers everything since previous exam, with emphasis on: parametric curves, vectors, lines, planes, velovity vectors, sketching surfaces, partial derivatives, chain rule. Exam 3makeup Show Work!! 1)(10) Does f ( x, y ) = ln( x 2 - y 2 ) satisfy the partial diﬀerential equation below? 2 f ∂x 2 - 2 f ∂y 2 = 0 2)(20) Let x + y - z = 3 and x - 3 y + 2 z = 1 be two planes. a) Do the planes intersect? b) If the answer to a) is yes, they intersect in a line; ﬁnd the direction of that line. If the answer to a) is no, show that the planes are parallel. 3)(20 points) Let ¯ r = e 2 t ¯ i - e t ¯ j a) Without plotting points, sketch the curve for
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Unformatted text preview: -∞ < t < ∞ b) Find the velocity vector at t = 0. c) Sketch the vector in b), with its tail at ¯ r (0) 4)(20) Let f ( x, y ) = xy ; x = u 2-v 2 , let y = u 2 + v 2 ; u = r + s ; v = r-s . a) Draw the tree diagram for these quantities b) State the chain rule for ﬁnding ∂f/∂s c) Use the chain rule to compute ∂f/∂s 5)(30) Let z = f ( x, y ) = x 2 . Let P = P (1 , 0) a) Sketch the surface b) Sketch the trace z = f ( x, 0), on the surface. c) Sketch the level curve z = 1, on the surface. d) Compute f x ( P ); f y ( P ). Referring back to b), c) explain why they have the value they do....
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