finalh.htm

Mathematics 2171-01
Calculus I
Spring 04
Dr. A. Shlapentokh
Final Examination

Suppose

and

, where

is a constant. Then what is

(a)	, where is a constant
(b)	, where is a constant
(c)	, where is a constant
(d)	, where is a constant
(e)	None of the above

Let

, where

is a constant. Then what is

(a)
(b)
(c)
(d)
(e)	None of the above

Suppose

. Then what is

(a)
(b)
(c)
(d)
(e)	None of the above

Suppose

. Then what

(a)	Cannot be determined from the given information.
(b)
(c)	, where is a constant.
(d)
(e)	None of the above

Suppose

. Then what

(a)	Cannot be determined from the given information.
(b)
(c)	, where is a constant.
(d)
(e)	None of the above

(a)	1
(b)	-1
(c)	0
(d)	2
(e)	None of the above

(a)	1
(b)	2
(c)	3
(d)	4
(e)	None of the above

(a)	21
(b)	22
(c)	23
(d)	24
(e)	None of the above

(a)	12/9
(b)	14/9
(c)	16/9
(d)	18/9
(e)	None of the above

10.

(a)	0
(b)	1
(c)	2
(d)	3
(e)	None of the above

11.

(a)
(b)
(c)
(d)
(e)	None of the above

12.

Suppose

. Then what is

(a)
(b)	where is a constant
(c)	Not enough information to determine.
(d)
(e)	None of the above

13.

Suppose

. Then what is

(a)	Not enough information to determine.
(b)	25/2
(c)	5
(d)	3/2
(e)	None of the above

14.

Suppose

. Then what is

(a)	Not enough information to determine.
(b)	, where is a constant
(c)	, where is a constant
(d)	, where is a constant
(e)	None of the above

15.

Suppose

. Then what is

(a)	Not enough information to determine.
(b)	, where is a constant
(c)	, where is a constant
(d)	, where is a constant
(e)	None of the above

16.

Suppose the radius of a circle is changing at the rate 2mm/min. Then find the rate of change for the area of the circle when the radius is 1 mm.

(a)	square mm/min.
(b)	square mm/min.
(c)	square mm/min.
(d)	square mm/min.
(e)	None of the above

17.

Find all the critical points of function

(a)	This function has no critical points.
(b)
(c)	is any integer.
(d)	is any integer.
(e)	None of the above

18.

Find all the critical points of the function

(a)	This function has no critical points.
(b)	is the only critical point.
(c)	is the only critical point.
(d)	and are the only critical points.
(e)	None of the above

19.

Find all the local maxima and minima for the function

(a)	No local maxima or minima
(b)	Local maximum at 2, local minimum at -2
(c)	Local maximum at -2, local minimum at 2
(d)	Local maximum at -2
(e)	None of the above

20.

Let

be a real number. Determine for which values of

the function

is always increasing?

(a)	There are no such values.
(b)
(c)	The function is always increasing for any value of .
(d)	Impossible to determine from given information.
(e)	None of the above

21.

Let

be a real number. Find all the values of

for which the function

always concaves up.

(a)	There are no such values.
(b)
(c)	The function always concaves up for any value of .
(d)	Impossible to determine from given information.
(e)	None of the above

22.

Let

be a real number. Which of the following statements is not true?

(a)	has a vertical asymptote .
(b)	has a horizontal asymptote .
(c)	has no asymptotes.
(d)	has no slant asymptotes.
(e)	None of the above

23.

Let

be a positive real number. Then the maximum value of the function

in the interval

(a)	does not exist.
(b)	is attained at one of the end points.
(c)	is attained at
(d)	is impossible to determine.
(e)	None of the above

24.

Which of the following graphs is a graph of a function with

(e)	None of the above

25.

Which of the graphs in Problem 24 is a graph of the function with

and

26.

Which of the graphs in Problem 24 is a graph of the function with

and

27.

Which of the graphs in Problem 24 is a graph of the function with

and

In Problems 28 – 35 compute the limits:

28.

(a)
(b)
(c)
(d)
(e)	None of the above

29.

(a)
(b)
(c)
(d)
(e)	None of the above

30.

(a)
(b)
(c)
(d)
(e)	None of the above

31.

(a)
(b)
(c)
(d)
(e)	None of the above

32.

(a)
(b)
(c)
(d)
(e)	None of the above

33.

(a)
(b)
(c)
(d)
(e)	None of the above

34.

(a)
(b)
(c)
(d)
(e)	None of the above

35.

(a)
(b)
(c)
(d)
(e)	None of the above

36.

Find the point on the line

which is the closest to the point

(a)	(1/2,3/2)
(b)	(1,2)
(c)	(3/2,5/2)
(d)	(2,3)
(e)	None of the above

37.

What should the length of the sides of a rectangle be if the area of the rectangle is 30 and the perimeter is supposed to be as large as possible?

(a)	10, 3
(b)	20, 3/2
(c)	30, 1
(d)	5, 6
(e)	None of the above

38.

What is a possible formula for

and a possible value for

(a)
(b)
(c)
(d)
(e)	None of the above

39.

What is a possible formula for

and a possible value for

(a)
(b)
(c)
(d)
(e)	None of the above

40.

What is a possible formulas for

and a possible value for

(a)
(b)
(c)
(d)
(e)	None of the above

41.

What is a possible formula for

and a possible value for

(a)
(b)
(c)
(d)
(e)	None of the above

42.

Find the average rate of change between

and

for the function

(a)
(b)
(c)
(d)
(e)	None of the above

43.

Find the average rate of change between

and

for the function

(a)
(b)
(c)
(d)
(e)	None of the above

44.

Find the average rate of change between

and

for the function

(a)
(b)
(c)
(d)
(e)	None of the above

45.

Find the the tangent line to

(a)
(b)
(c)
(d)

46.

Suppose the position of a particle moving in a straight line is given by

. Find the total distance travelled by the particle between

and

(a)	0 units
(b)	1 units
(c)	2 units
(d)	3 units
(e)	None of the above

47.

Suppose

is a differentiable function of

. Find

and

(a)	-1
(b)	0
(c)	1
(d)	Cannot be determined from the given information.
(e)	None of the above

48.

Which of the following statements is true for

(a)	.
(b)	.
(c)
(d)	does not exist because the left limit does not exist.
(e)	None of the above

49.

Which of the following statements is true for

(a)	This function is continuous at 0.
(b)	This function is not continuous at 0 because does not exist.
(c)	This function is not continuous at 0 because the function is undefined at 0.
(d)	This function is not continuous at 0 because even though exists, .
(e)	None of the above

50.

Which of the following statements is true for

(a)	This function is continuous at 0.
(b)	This function is not continuous at 0 because does not exist.
(c)	This function is not continuous at 0 because the function is undefined at 0.
(d)	This function is not continuous at 0 because even though exists, .
(e)	None of the above

51.

Which of the following statements is true for

(a)	This function is continuous at 0.
(b)	This function is not continuous at 0 because does not exist.
(c)	This function is not continuous at 0 because the function is undefined at 0.
(d)	This function is not continuous at 0 because even though exists, .
(e)	None of the above