MATH140 Exam 1 - Express the distance between

MATH140 Exam 1 

1) Express the distance between the point (3, 0) and the point of the parabola as a function of .

1) _____________

2) If and , find and .

2) _____________

3) Sketch the graph of the function. Indicate any points of discontinuity. Explain precisely why your choice of points is/are in fact discontinuities.

3) _____________

4) Sketch the translated circle . Indicate the center and radius.

4) _____________

5) According to the National Highway Traffic Safety Administration, the number of individuals arrested A(t) for driving under the influence of alcohol as a function of their age t is indicated in Table 1. Use the data in Table 1 to:

(I) Estimate the average rate of change in the number of arrests (per 100,000 drivers) for driving under the influence of alcohol between the ages of 18 and 26.

(II) Estimate the instantaneous rate of change at the age of 40 and interpret your answer.

Table 1

Age

(years)

Number of Arrests

(per 100,000)

14

113.00

16

308.77

18

421.32

20485.32

22

519.13

24

534.54

26

537.99

28

533.67

30

524.25

32

511.47

34

496.52

36

480.17

38

462.97

40

445.30

42

427.40

44

409.45

46

391.59

48

373.89

50

356.41

52

339.18

54

322.23

56

305.57

58

289.21

60

273.14

5) _____________

(Write Solution on next page:)

Solution to #5:

6) Evaluate . 6) _____________

(A) 2/3 (B) 1 (C) 3 (D) does not exist (E) none of the above

7) Given G( x) = , tell where G is continuous. (Give your answer in interval form.)

7) _____________

(A) (-,)

(B) (-5, 5)

(C) (-, 5) (5, )

(D) (-, 0) (0, )

(E) none of the above

8) Given f( x) = , find all points where f is not continuous. For each such point, tell whether or not the discontinuity is removable or not removable. Explain why the point is a discontinuity and then explain why it is a removable or non-removable discontinuity.

8) _____________

(A) 0; removable discontinuity

(B) 0; not removable discontinuity

(C) -2, 2, 0; removable discontinuity

(D) -2, 2, 0; not removable discontinuity

(E) none of the above

9) Find the trigonometric limit: . 9) _____________

(A) 0 (B) 3/2 (C) 1 (D) does not exist (E) none of the above

10) Given L( x) = , tell where L is continuous. (Give your answer in interval form.)

10) ____________

(A) 0

(B) 1

(C) (-, 0) (0, )

(D) (-,)

(E) none of the above

11) State whether the function f( x) = 3 – x2 attains a maximum value or a minimum value (or both) on the interval [-2, 2).

11) ____________

(A) max at 0; min at -2

(B) max at 0

(C) min at -2

(D) min at 0, max at -2

(E) none of the above

12) Find given

13) Find given . 13) ____________

14) Find given

15) When a person gets a single flu shot, the concentration of the drug in milligrams per liter after t hours in the bloodstream is modeled by the following equation. Find the horizontal asymptote of the function F(t) and interpret what the horizontal asymptote represents with respect to the concentration of flu medication in the bloodstream as time passes.

F(t) =

15) ____________

16) After studying calculus for a while, you decide to make a pot of coffee. You pour the coffee grounds into a cone-shaped filter whose radius is 3 cm and height 6 cm. If the coffee grounds are being poured into the filter at a rate of 4 cm3/s, then what is the rate at which the depth of the coffee grounds is rising when they are 2 cm deep?

16) ____________