hw14 more e3 practice - This Week exam iii 15.8 p976 3, 5,...

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Unformatted text preview: This Week exam iii 15.8 p976 3, 5, 7, Exam 3 40, SHOW WORK!! 9, 15, 17, 25, 41 1)(20) Find a Thursday April 28 plane through P (1, 0, 0), containing the line Cheat Sheets OK, No z = t, and also perpendicular to the plane x = 1, y = 1 − t, Calculators Covers §§11.1, 11.2,t11.3, ,13.1, 13.2, 13.3, 13.4, 13.5, 14.1, 14.2, 15.1, 15.2, 15.3, ¯ = s(1, 1, 0) + (0, 1 1) r 15.4, 15.5, 15.6 Hw 14 more pracTice Let f (x, y ) =(x2 y ) y 2 ln(x 2 − y 2 ). Does f = P (1, 1) partial differen2)(20) Let f x, − = − x + y , and let P satisfy the a) Find f and f (P ). tial equation b) In the xz plane, draw the trace z = f (x, 1) and mark P . ∂f ∂f y trace z = = 0 c) In the yz plane, draw the∂x − x ∂y f (1, y ) and mark P . d) Referring to the graphs in b) and c), discuss why f (P ) has the value it does. 3)(60) Let z = f (x, y ) = x2 + y 2 ; P = P ( 1 , 1 ) 22 a) Sketch the surface; locate the P and f (P ). b) Find c) Sketch f; f (P ). f (P ) on the graph in a), with its tail at P . f (P ) with its tail at P . d) In the xy plane, draw the level curve z = f (x, y ) = f (P ). e) On the graph in d), locate P and draw f) Redraw the graph in a). On the new graph, draw the trace z = f (x, 1 ). 2 4)(20) Let z = f (x, y ); x = r cos θ, y = r sin θ. a) Draw the tree diagram for these quantities b) State the chain rule for finding ∂f /∂r c) Use the chain rule to compute ∂f /∂r. ( you don’t have a formula for f , so you can’t simplify partials for f ). 1 5)(30) Let z = f (x, y ) = 1 − x2 − y 2 . Let P = P (0, √2 ) a) Sketch the surface 1 b) Sketch the trace z = f (x, √2 ) on the surface. Locate P . 1 c) Sketch the trace z = f (x, √2 ) in the xz plane. Locate P . c) Sketch the trace z = f (0, y ), in the yz plane; locate P . d) Compute fx (P ). Referring back to c), explain why it has the value it does. ...
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