problem_10 - shin (ys5232) – Homework 10 (Quest) –...

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Unformatted text preview: shin (ys5232) – Homework 10 (Quest) – miner – (55096) This print-out should have 6 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 Find dy/dx when x3 − 2y 3 + 9xy + 1 = 0 . x2 + 3 y dy = 1. dx 2y 2 − 3x 2. dy 3 y − x2 = dx 2y 2 − 3x dy dx dy dx dy dx dy dx dy dx 10.0 points y x −1 dy 6. = dx 1− x y 1 003 10.0 points If y = y (x) is defined implicitly by 2y 2 − xy − 28 = 0, find the value of dy/dx at (10, 7). 1. (10, 7) =− = = 4 9 2. x2 − 3 y dy = 3. dx 2y 2 − 3x 4. x2 − 3 y dy = dx 2y 2 + 3x (10, 7) 7 18 4 9 7 18 3. (10, 7) 4. dy 3 y + x2 5. = dx 2y 2 + 3x 002 Find dy/dx when √ y + x = 2 xy . y x +1 dy 1. = dx 2− x y y x +1 dy = 2. dx 1− x y y x −1 dy = 3. dx 2+ x y (10, 7) =− = 5. 10.0 points (10, 7) 7 19 10.0 points 004 Find dy when dx tan(xy ) = 3x + y . 3 + y sec2 (xy ) dy = dx x sec2 (xy ) − 1 1 − x sec2 (xy ) dy = dx y sec2 (xy ) + 3 dy 3 − y sec2 (xy ) = dx x sec2 (xy ) + 1 1 − x sec2 (xy ) dy = dx y sec2 (xy ) − 3 3 − y sec2 (xy ) dy = dx x sec2 (xy ) − 1 1 + x sec2 (xy ) dy = dx y sec2 (xy ) + 3 1. 2. 3. 4. −1 dy = dx 1+ x y y x 4. 5. y x +1 dy = 5. dx 2+ x y 6. shin (ys5232) – Homework 10 (Quest) – miner – (55096) 005 10.0 points 2 Determine dy/dx when 5 cos x sin y = 6 . dy dx dy dx dy dx dy dx dy dx 1. 2. 3. 4. 5. = tan x tan y = cot x cot y = tan x = tan xy = cot x tan y 006 10.0 points Find the equation of the tangent line to the graph of 4y 2 − xy − 9 = 0, at the point P = (9, 3). 1. 14y + 3x = 15 2. 14y = 3x + 15 3. 3y = x 4. 5y = x + 6 5. 5y + x = 6 ...
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This note was uploaded on 10/06/2010 for the course M 480N taught by Professor Guntel,miner during the Fall '10 term at University of Texas at Austin.

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problem_10 - shin (ys5232) – Homework 10 (Quest) –...

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