Math 114

Answers to even problems

 

 

Section 9.4

6. x2/16+y2/4=1, ellipse

36. x=aΘ-bsin(Θ), y=a-bcos(Θ)

 

Section 9.5

2. –8

18. 7

24. 28π/9

 

Section 9.6

6. a) (1,1) b) (1,0) c) (0,0) d) (-1,1) e) (3sqrt(3)/2, -3/2) f) (3,4) g) (1,0)

h) (-sqrt(3),3)

60. r=10cos(Θ)

 

Section 9.9

30. πsqrt(5)(eπ/2+1)

 

Section 10.1

20. u=-1/sqrt(2)i-1/sqrt(2)j

30. tangent vector 1/sqrt(34)(5i+3j), normal vector 1/sqrt(34)(-3i+5j)

 

Section 10.3

8. AB=2, |A|=sqrt(2), |B|=sqrt(3), cos(Θ)=sqrt(2/3), |B|cos(Θ)=sqrt(2), projAB=i+k

 

Section 10.4

6. AxB=j, BxA=-j

 

Section 10.5

6. x=3+2t, y=-2-t, z=1+3t

 

Section 10.7

    Rectangular    Cylindrical    Spherical

2.     (1,0,0)             (1,0,0)           (1,π/2,0)

4.     (0,0,1)             (0,0,1)           (1,0,0)

6.     (sqrt(2),0,1)    (sqrt(2),0,1)   (sqrt(3),cos(1/sqrt(3)),0)

8.     (0,-3/2,sqrt(3)/2) (3/2,3π/2,sqrt(3)/2) (sqrt(3),π/3,-π/2)

10.   (0,0,-sqrt(2))   (0,0,-sqrt(2)) (sqrt(2),π,3π/2)

32. A cone with vertex (0,0,4) (rectangular) and base the circle x2+y2=16 in the xy-plane

40. Right circular cylinder parallel to the z-axis generated by the circle r=2cos(Θ) in the rΘ-plane