Calculus 1 Science
Winter 1998
Final Exam Answers
1a) does not exist
1b) -1
1c) 2
1d) -4
1e) does not exist
1f) -1.5
1g) -¥
1h) -2
1i) -¥
1j) -3
1k) does not exist
1l) x = 4
2a) 10
2b) 0.196
2c) 7
2d) 0
2e) -¥
3) A = -12
B = 30
4) Use the limit as h goes to 0 definition to get
5a)
5b)
5c)
5d)
5e)
6)
7) 2/5
8) (1, -7) and (-2, 20)
9a) velocity = -5.4 t + 27
acceleration = -5.4
9b) At t = 5 seconds, height is 73.5 feet
10) Absolute max at x = 2 is 31
Absolute min at x = 5 is -50
11a) x-intercepts: 1.15 and -1.15
y-intercepts: none
11b) Vertical asymptote: x = 0
Horizontal asymptote: y = 0
11c) Critical numbers: 2 and -2
11d) relative max: (2, 1)
relative min: (-2, -1)
11e) interval of increase: (-2, 0) and (0,2)
11f) intervals of downward concavity: (-¥ , -2.828) and (0, 2.828)
11g) Points of Inflection: (2.8, 0.88) and (-2.8, -0.88)
11h)
12)
where x is the length of the base, or the co-ordinate of the right vertex
13)
14a)
14b) -csc x - cot x + C
14c)
14d)
15) 19.3333 square units