Math 120b Exam 1 Solutions
1. (a) A line is parallel to a plane if the direction vector of the line is perpendicular to
the normal vector of the plane. The direction vector of this line is 1, 0, 1 ; the normal
vector of this plane is 1, 2, 1 . Because 1,
Math 120b Exam 2 Solutions
1. In the rst quadrant, the curves y = 4 x2 and y = 1 x2 are the portions of the
circles of radius 2 and 1 in the rst quadrant. That is, the region has this form.
The natural coordinate system for this region is polar, and the r
Math 120b Exam 2
1. Suppose is the portion of the rst quadrant bounded by y =
Evaluate
1
dA
x2 + y 2
2. Evaluate
/2
/2
y
0
y2
4 x2 and y =
1 x2 .
sin(x)
dxdy
x
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0.
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