ex4_fall11_2313

# ex4_fall11_2313 - Name MAC 2313 Exam 4 Version A SHOW ALL...

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Name: MAC 2313 Exam 4 Version A 10/17/2011 SHOW ALL YOUR WORK. Answers without procedure will be graded zero. [5] 1.The radius r and height h of a cylinder change with time. At a certain instant the dimensions are r = 1 and h = 6, and r is increasing at a rate of 2 m/s while h is decreasing at a rate of 1 m/s. At that instant ﬁnd the rate at which the volume of the cylinder is changing. [5] 2. Find ∂z ∂u , if z = cos x sin y , x = u - v and y = u 2 + v 2 . Express your answer in terms of u and v . [5] 3. Suppose that z = z ( x,y ) ( z is implicitly deﬁned as a function of x and y ), and also y = y ( x,z ) through some equation F ( x,y,z ) = 0. Suppose that at some point P , F x = 2, F y = - 4 and F z = 3, which of the following is the smallest at P ? ∂z ∂y , ∂z ∂x or ∂y ∂x

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[5] 4. Find the directional derivative of f ( x,yz ) = z 2 e xy at the point ( - 1 , 0 , 3), in the direction of v = h 3 , 1 , - 5 i [5] 5. What is the maximum value of the directional derivative of f ( x,y,z
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ex4_fall11_2313 - Name MAC 2313 Exam 4 Version A SHOW ALL...

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