Exam2Solutions - Math 212, Fall 2011 Name: _ Exam 2 1. [18...

Math 212, Fall 2011
Name: __________________________________
Exam 2
1. [18 points (9 pts each)]
(a) Find the equation of the tangent plane to the surface at the point . b
(b) Find parametric equations for the line tangent to the curve at the point . r a b a b > œØ >ß$/ ß/ Ù !ß$ß" sin
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Math 212, Fall 2011 Exam 2 2
2. In the figure to the right, a circle of radius 1 is [10 points]
tangent to a perpendicular pair of line segments. Find the
coordinates of the center of the circle.
LParen1 0,0 RParen1
LParen1 3,1 RParen1
3. Find the distance from the line to the plane .

Math 212, Fall 2011 Exam 2 3
4. Let be the plane , and let be the plane . Find the equation of [10 points] T #B$CD œ& U C$D œ""
the plane through the point that is perpendicular to both and . a b "ß#ß$ T U

Math 212, Fall 2011 Exam 2 4
5. [16 points (8 pts each)]
(a) Evaluate , where is the region inside the cylinder and between the planes
I
$ # #
< D.Z I B C œ"
D œ! D œ" and
(b) Evaluate , where is the solid hemisphere defined by and .
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.