ma166FinalExReview - MA 166 FINAL EXAM PRACTICE PROBLEMS...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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).
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This document was uploaded on 01/21/2012.

Page1 / 4

ma166FinalExReview - MA 166 FINAL EXAM PRACTICE PROBLEMS...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online