MA 124 Fall-08, Exam 1 Answers
- 1) The graph is the same as 5.4/20 .
- 1 a) Local Max: x - 2, 6, 10 . Local Min: x = 4, 8 .
- 1 b) At x = 2.
- 1 c) On (1, 3) , (5, 7) , (9, 10)
- 2) pi/2
- 3) 2xe^(x/2) -4e^(x/2) + C
- 4) - 1/(2x) - (1/4) sin(2/x) + C
- 5) ln(3/8)
- 6) It is improper since 1/sqrt(x+2) is not continuous where sqrt(x+2) =
0 , which occurs when x = -2 , which is in the range of integration.
We must write the integral as the limit as a -> -2^+ of the integral from a to
0.
The limit exists, hence the integral converges.
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