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Practice Midterm 2 #2

# Practice Midterm 2 #2 - University of Pennsylvania Maths...

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University of Pennsylvania Maths 114 Fall 2005 Practice for Exam II Instructions: There are twenty-three questions on this exam, of which you need only to do twenty in order to obtain full marks. 1. Consider four functions a, b, c, d whose assignment rules are given by a ( x, y ) = x y, b ( x, y ) = x + y, c ( x, y ) = x 2 y, d ( x, y ) = x y 2 , and the four contour plots I, II, III, and IV in figures 1 through 4 . Which of the following matches is correct? –10 –5 5 10 y –10 –5 5 10 x Figure 1: I –10 –5 5 10 y –10 –5 5 10 x Figure 2: II –10 –5 5 10 y –10 –5 5 10 x Figure 3: III –10 –5 5 10 y –10 –5 5 10 x Figure 4: IV A ( a , III), ( b , II), ( c , I), ( d , IV) B ( a , II), ( b , III), ( c , I), ( d , IV) C ( a , III), ( b , II), ( c , IV), ( d , I) D ( a , II), ( b , III), ( c , IV), ( d , I) E none of these Office: 2C7 http://www.math.upenn.edu/ ˜ santosan k [email protected]

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University of Pennsylvania Maths 114 Fall 2005 Practice for Exam II 2. Let f ( x, y ) = x + y x 2 y . Which of the following assertions is false? A lim ( x,y ) (0 , 0) y =0 f ( x, y ) = 1 B lim ( x,y ) (0 , 0) f ( x, y ) does not exist C lim ( x,y ) (0 , 0) y = x f ( x, y ) = 2 D lim ( x,y ) (0 , 0) x =0 f ( x, y ) = 1 E all of them are true 3. Which of the following limits is correct? A lim ( x,y ) (0 , 0) x 2 y ( y 1)( x 2 + y 2 ) = 0 B lim ( x,y ) (1 , 2) 4 x + 2 1 x + y 2 = 2 C lim ( x,y ) (0 , 0) x 2 + y 2 x 2 y = 0 D lim ( x,y ) (0 , 0) 2 x y 2 2 x 2 + y = 1 E all are incorrect 4. Find the tangent plane to the surface x 2 + y 2 z 2 = 0 at the point (3 , 4 , 5) .
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Practice Midterm 2 #2 - University of Pennsylvania Maths...

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