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Unformatted text preview: i f ( x, y ) = (0 , 0) . (a) Compute the partial derivative ∂f ∂y at points % = (0 , 0). (b) Is f continuous at (0 , 0)? Explain your answer. (c) Do the partial derivatives of f exist at (0 , 0)? Explain your answer. 6. (Homework Exercises, Sections 14.4, 14.5) (a) The equation F ( x, y, z ) = sin( x + y )+sin( y + z )+sin( x + z ) = 0 implicitly de±nes z as a function of x and y . Find the value of ∂z ∂x at the point ( π, π, π ). (b) Let g ( x, y, z ) = xe y + z 2 . Find the direction in which g increases most rapidly at the point P = (1 , ln 2 , 1 / 2). 7. The plane L is tangent to the sphere x 2 + y 2 + z 2 = 1 at the point P = ³ 1 3 , √ 8 3 , ´ . The plane L is also tangent to the sphere ( x − a ) 2 + y 2 + ( z − c ) 2 = 4 at the point Q = ³ − 7 3 , 2 √ 8 3 , ´ . Find a and c ....
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This test prep was uploaded on 09/23/2007 for the course MATH 1920 taught by Professor Pantano during the Fall '06 term at Cornell University (Engineering School).
 Fall '06
 PANTANO
 Derivative, Multivariable Calculus, Vectors, 2J, Prelim Exam, arc length parameter

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