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math200_december1999

math200_december1999 - MATH 200-Calculus III(December 1999...

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MATH 200 —Calculus III (December 1999) Closed book examination. Time: 2.5 hours. Special Instructions: Calculators are NOT required but may be used. Books or notes are NOT permitted. Show your work in the spaces provided. 1) [10 marks] Answer each of the following with either true [T] or false [F]. Reasons need not be given. No credit for ambiguous or wrong answers. a) Let a and b be vectors in R 3 . If c a b a = then b = c . b) If a and b are parallel vectors in R 3 , then a x b = 0 . c) . 1 ) sin( lim ) 0 , 0 ( ) , ( = x xy y x d) The equation x 2 + y 2 = 0 describes a line in xyz -space. e) The space curve parametrized by k j i r t t t t + + = ) (cos ) (sin ) ( lies on the cylinder 1 2 2 = + y x . f) If a function f = ( x , y , z ) has directional derivative 0 ) , , ( 0 0 0 = z y x f D u for all unit vectors u , then ) , , ( 0 0 0 z y x is a critical point of f . g) Assuming f = f ( t ) is a differentiable function and g ( x , y ) = f ( xy ), then ) ( ' xy yf x g = . h) The function
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math200_december1999 - MATH 200-Calculus III(December 1999...

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