MATH 126 Final: MATH 126 UW Final Exam Spring 2012 Solutions
FINAL EXAM ANSWERS
MATH 126 SPRING 2012
1. 2x−8y−5z+ 14 = 0
2. (a) i. parabolas
ii. parabolas
iii. hyperbolas
(b) hyperbolic paraboloid
(c) (4,2,4) and (−10,−5,25)
3. (a) aT=18
√π2+9
(b) π
(c) θ= cos−16π
√π2+ 144√37≈76◦
4.
Function z= 5x+ 3y z = (x2+y2)0.1z= cos(4x+ 2y)z=x2+y2z= 2x2−3y2
Graph G5 G1 G4 G2 G3
Contour Map C2 C3 C1 C4 C5
5. (a) P(1,1,2) and R(1,1,−2)
(b) 2x+ 3y−2z= 1
6. .
(6,0)
(8,4)
(0,2)
y= 2 −x
3
x= 3(2 −y)
y= 2 + x
4
x= 4(y−2)
y= (x−6)2
x= 6 + √y
ZZD
f(x, y)dA =Z2
0Z6+√y
3(2−y)
f(x, y)dx dy +Z4
2Z6+√y
4(y−2)
f(x, y)dx dy
Document Summary
Math 126 spring 2012: 2x 8y 5z + 14 = 0. 2. (a: parabolas, parabolas, hyperbolas (b) hyperbolic paraboloid (c) (4, 2, 4) and ( 10, 5, 25) (a) at = 18 (b) . Contour map z = 5x + 3y z = (x2 + y2)0. 1 z = cos(4x + 2y) z = x2 + y2. C5 (a) p (1, 1, 2) and r(1, 1, 2) (b) 2x + 3y 2z = 1. 4 x = 4(y 2) (8, 4) y = (x 6)2 x = 6 + y (6, 0) f (x, y) dx dy (0, 2) y = 2 x x = 3(2 y) Zzd f (x, y) da = z 2. 3(2 y) f (x, y) dx dy +z 4. 4(y 2: hint: the volume of the cylinder is r2h, where r = 20 and h = 20. So, the volume of the cylinder is 400 .
