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Chapter 2 / Exercise 73
College Algebra
Gustafson/Hughes
Expert Verified
Answer(s) submitted: 0 1/2 (correct) Correct Answers: 0 1/2 49. (1 pt) Consider the function f whose graph is shown below. This function is given by f ( x , y ) = ( 6 xy x 2 + y 2 , ( x , y ) 6 = ( 0 , 0 ) 0 , ( x , y ) = ( 0 , 0 ) (a) Find a formula for the single variable function f ( 0 , y ) . f ( 0 , y ) = What is f ( 0 , 0 ) for this function? f ( 0 , 0 ) = Find its limit as y 0: ım y 0 f ( 0 , y ) = (b) Based on your work in (a) , is the single variable function f ( 0 , y ) continuous? ?
(e) Finally, consider f along rays emanating from the origin. (Notice that this means that y = x is a contour of f. Be sure you can explain why this is.)
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Chapter 2 / Exercise 73
College Algebra
Gustafson/Hughes
Expert Verified
Find and simplify f on any ray y = mx . f ( x , mx ) = (Again, notice that this means that any ray y = mx is a con- tour of f; be sure you can explain why.) (correct) (f) Is f ( x , y ) continuous at ( 0 , 0 ) ? ? SOLUTION 50. (1 pt) f u ( 3 , π ) = D u f ( 3 , π ) = 759.94 (correct) 51. (1 pt) Suppose f ( x , y ) = p tan ( x )+ y and u is the unit vector in the direction of h 0 , 1 i . Then, 52. (1 pt) Suppose f ( x , y ) = 4 x 2 + y 2 and u is the unit vector in the direction of h- 3 , 2 i . Then, (c) f u ( 3 , π ) = D u f ( 3 , π ) = 16
(correct) Correct Answers: <-2*y/(xˆ2)*cos(2*y/x),2*x/(xˆ2)*cos(2*y/x)> <0.349066,-0.333333> -0.0111246 54. (1 pt) View the curve ( y - x ) 2 + 2 = xy - 3 as a contour of f ( x , y ) . (a) Use f ( 2 , 3 ) to find a vector normal to the curve at ( 2 , 3 ) .