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Unformatted text preview: dy/dx in terms of x and y . (a) √ x + √ y = 9 (b) x 2x 2 y + xy 2 + y 2 = 1 (c) ( y + 3 x ) 24 x = 0 7 (6) Use implicit diﬀerentiation to obtain dy/dx in terms of x and y . (a) e sin y = x 3 arctan y (b) ln ( x 2 ) + ln ( y 3 ) = 10 (c) cos 2 y + sin 2 y = y + 2 8 (7) Given x 3 y + xy 3 = 2, ﬁnd y and y 00 at the point (1 , 1). 9 (8) Prove that the lines tangent to the curves 5 y2 x + y 3x 2 y = 0 and 2 y + 5 x + x 4x 3 y 2 = 0 at the origin intersect at right angles....
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 Spring '09
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 Calculus, Derivative, #, Mathematical analysis, Convex function, Polytechnic Institute of NYU MA

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