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
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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 thecoordinates of the center of the circle.
3. Find the distance from the line to the plane .[10 points]
Math 212, Fall 2011
Exam 2
3
4. Let be the plane , and let be the plane . Find the equation of
[10 points]
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the plane through the point
that is perpendicular to both
and
.
a
b
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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 planesI$##< D.ZIB C œ"D œ!D œ"and
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.
(b) Evaluate , where is the solid hemisphere defined by and .
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