Calculus 1 Science

Winter 1998

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