Math54 LE1 2nd Sem 2012-2013
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Transcript of Math54 LE1 2nd Sem 2012-2013
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7/29/2019 Math54 LE1 2nd Sem 2012-2013
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Mathematics 54
First Long Exam
1. Evaluate the following integrals. (6 points each). 2 sin 6 cos 6
0
. 2 5
. 4
(2 1)( 2 2) . ||
+
2. Solve the differential equation: (6 pts.) = (1 9)(ln)
3. Find the orthogonal trajectories for the family of curves: (5 pts.) = 1 ; >
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7/29/2019 Math54 LE1 2nd Sem 2012-2013
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Answer Key
1. Evaluate the following integrals. (6 points each). 2 sin 6 cos 6 =
0
. 2 5 = ( ) ( ) .
4(2 1)( 2 2) =
| |
. || = +
2. Find a particular curve from this family of curves that contains (1,0). (6 pts.) = (1 9)(ln)
() = 3. Find the orthogonal trajectories for the family of curves: (5 pts.)
= 1 ; >
=
TOTAL: 35 pts.
GOOD LUCK!!!
