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ma166FinalExReview

# ma166FinalExReview - MA 166 FINAL EXAM PRACTICE PROBLEMS...

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MA 166 FINAL EXAM PRACTICE PROBLEMS Spring 2010 1. If ~a = ~ i + ~ j + ~ k and ~ b =2 ~ i - ~ k , ﬁnd the vector projection of ~ b onto ,proj ~ b . A. 1 3 B. 1 3 C. 1 5 D. 1 3 ~ b E. 1 3 ~ b 2. Find the angle between the vectors = - ~ i +2 ~ j and ~ b = ~ i +3 ~ j A. 3 π 4 B. π 4 C. 2 π 3 D. 5 π 6 E. 11 π 12 3. Find the area of the triangle with vertices at the points (1 , 0 , 2) (2 , 4 , - 3) and (1 , 2 , 1). A. 1 2 41 B. 41 C. 10 D. 2 2 21 E. 41 2 4. If = ~ i - ~ j and ~ b ~ j - ~ k , ﬁnd a unit vector orthogonal to both and ~ b . A. 1 2 ( ~ i + ~ j )B . 1 6 ( ~ i + ~ j ~ k )C . 1 5 ( ~ j ~ k )D . ~ i + ~ k E. 1 5 ( ~ i ~ k ) 5. The radius of the sphere x 2 + y 2 + z 2 x +4 y - 6 z =3is A. 3 + 13 B. 13 C. 65 D. 3 + 56 E. 17 6. The area of the region enclosed by the curves y = x 2 +1and y x +9isgivenby A. Z 4 - 2 ( x 2 +1 - 2 x - 9) dx B. Z 4 - 2 (2 x +9 - x 2 - 1) dx C. Z 2 - 2 (2 x - x 2 - 1) dx D. Z 2 - 4 (2 x - x 2 - 1) dx E. Z 2 - 4 ( x 2 - 2 x - 9) dx 7. The volume of the solid obtained by rotating about the x –axis the region in the ﬁrst quadrant bounded by the graphs of y =1 - x 2 , y x ,and x =0isgivenby A. 2 - 1 Z 0 (1 - x 2 - 2 x ) dx B. 2 - 1 Z 0 π (1 - x 2 x ) dx C. 0 Z - 2 - 1 π [(1 - x 2 ) 2 - (2 x ) 2 ] dx D. 2 - 1 Z 0 π [(1 - x 2 ) 2 - (2 x ) 2 ] dx E. 2 - 1 Z 0 [(2 x ) 2 - (1 + x 2 ) 2 ] dx 8. Let R be the region bounded by the curves y = x 2 and y x . Using the method of cylindrical shells, the volume of the solid generated by rotating R about the x –axis, is given by A. 2 Z 0 π (2 x - x 2 ) dx B. 2 Z 0 2 π (2 x - x 2 ) 2 dx C. 2 Z 0 πx 2 ( x 2 - 1 2 x ) dy D. 4 Z 0 πy 2 ( 1 2 y - y ) dy E. Z 4 0 2 ( y - 1 2 y ) dy 9. A right circular conical tank of height 20 ft. and base radius 5 ft. has its vertex at the bottom, and its axis vertical. If the tank is full of water at 62.5 lb./cu. ft., the work required to pump all the water over the top is: (Take the y -axis upwards along the axis of the tank and the origin at its vertex).

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ma166FinalExReview - MA 166 FINAL EXAM PRACTICE PROBLEMS...

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