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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 Fall '06
 PANTANO
 Derivative, Multivariable Calculus, Vectors, 2J, Prelim Exam, arc length parameter

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