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222-passman-06fafin

# 222-passman-06fafin - Math 222 Your Name T.A.’s Name Do...

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Unformatted text preview: Math 222 Your Name T.A.’s Name Do all 9 problems and show all work. Otherwise full credit Will not be given. Final Exam Passman l. a) Compute the deﬁnite integral ‘ 7r/4 / xsec2xdq: o b) Find the antiderivative /Z\$\\-— x2+1 ~ 1m 2)“z 3. Sketch the polar curve, I 7" = 23in 36 being sure to indicate where the curve exists. Find the area surrounded by one of its loops. 4. The polar curve 1 r=————' ﬁ+cos€ is an ellipse. a) Write this curve as a quadratic expression in terms of the a: and y coordinates, and ﬁnd the center of the ellipse. b) Where does the ellipse intersect the polar curve r=\/§—cos6i 5. Triangle OAB has vertices O(0,0,0), A(2,—2, 1) and B(6,2,3). Find its area and perimeter. Determine the angle at O, that is the angle between lines 0A and OB. ' 6. Find the equation 'of the plane containing the point P(4, 3, 1) and perpen— dicular to the line given by I xz2t+1 y23t+1 z=t—1 Find the point of intersection of the line and plane. 7. Given the vectors b) Determine the equation of the line perpendicular to both 27 and ”LB and passing through the point P(3, 2, 1). ‘ (3) Compute the volume of the parallelepiped determined by 27, 27 and 711'. 8. A particle moves through 3—space with velocity vector 27 2 (at cost) 7+ (615 sint) j’+ (2et) I; Find ds/dt, f, [<3 and N - 9. A moving particle in 3-space. has position vector F: 7+ tj’+ (752/2) E Find '17, if, 14;, cm and (LT. ...
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222-passman-06fafin - Math 222 Your Name T.A.’s Name Do...

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