Math NYA

Calculus 1 for Science

Final Exam Fall 2001

Answers

1ai) -2

1bii) - infinity

1ciii) 2

1b) limit is 3, value is 2, they are not equal

1c) removable

2a) ¼

2b) - infinity

2c) 10

2d) - infinity

3) continuous everywhere except x = 3

4a) When t = 4, s’ = 0

4b) s” = 32 m/s/s

5a) Use limit as h approaches 0 to get –2(x+1)^-2

5bi)

5bii)

5biii)

5biv) 2cos(Ax+B) (- sin(Ax+B) ) A

5bv)

6) sec x tan³x +5 sec³x tan x

7)

y = -2ex + 3e

8) x = 2 / 5 or 1 or 16 / 25

9) 100 m by 63.66 m

10) Absolute max is 149

Absolute min is – 75

11) decreasing at m/h

12)

x-intercepts: (-1,0) , (2, 0)

y-intercept (0, 2)

vertical asymptote at x = 1

horizontal asymptote at y = -1

min at ( 5, -1.125)

no local max

Point of inflection (7, -1.1111)

increasing for x < 1 and 5 < x

decreasing for 1 < x < 5

cc up for x < 1 and 1 < x < 7

cc down for 7 < x

13)

14a)

14b) 2sec x –5 tan x + C

14c)

15) 4.5

16) -3 cos x – 2 sin x + 4x + 6