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Name:    Calculus test Chapter 3

Multiple Choice   (2 Marks Each) Identify the letter of the choice that best completes the statement or answers the question.
A B C D	1.	Consider the function . Let P and Q be two points on the graph of f(x). The limit of the slope of the secant PQ, as Q approaches P along the graph, is a. undefined b. the slope of the tangent to the graph of f(x) at P c. the slope of the tangent to the graph of f(x) at Q d. the slope of the tangent to the graph of f(x) at the midpoint between P and Q
A B C D	2.	The average rate of change of a function f over an interval [3, 5] is a. the average of the function values, that is b. the limit of the values of the function as 5 approaches 3 c. the limit of the slopes of the tangents to the graph of f between 3 and 5 d. the slope of the secant joining the points and
A B C D	3.	The average rate of change of a function f over an interval [2, 5] is a. c. b. d.
A B C D	4.	The function f is continuous at a number a if a. it is continuous as x approaches a from both sides b. c. is defined d. is defined for values of x near a, even though might be undefined
A B C D	5.	The limit laws a. are obeyed only by differentiable functions b. are obeyed only by continuous functions c. express the limits of combinations of functions in terms of limits of the individual functions d. express the conditions for which taking a limit is valid
A B C D	6.	The function f has a jump discontinuity at a number a if a. exists c. is undefined b. d.
A B C D	7.	A rational function a. is continuous for all values of x in its domain b. is continuous at all values of x except those for which it has turning points c. has infinite discontinuities as its end behaviours d. is continuous at every value of x
A B C D	8.	Consider the position-time graph of an object moving in a straight line. The instantaneous velocity of the object at time t is a. the slope of the tangent at b. the limit of the slopes of secant lines over the intervals and as h approaches 0 c. d. all of the above
A B C D	9.	Consider the graph of a function . The instantaneous rate of change of the function at x is a. the slope of the tangent at x b. the limit of the slopes of secant lines over the intervals and as h approaches 0 c. d. all of the above
A B C D	10.	Consider the graph of a function . A valid expression for the instantaneous rate of change of the function at x is a. c. b. /20 d. all of the above
Short Answer (5 marks each)
	11.	a)  Determine the slope of the tangent to the graph of at the point (9, 2). b) Determine the equation of the tangent in part a).
	12.	Find , if it exists.
	13.	Find , if it exists.
Problem (10 marks each)
	14.	a) Determine the slopes of the tangents to the graph of at the points (0, 0), (1, 1), (2, 4), and (3, 9). b)  Graph the function and the tangents from part a).
	15.	a) Determine the slope of the tangent to the graph of at the general point whose x-coordinate is a. b) At which point on the graph of the function of part a) is the tangent parallel to the line ?
	16.	Determine the values of x, if any, for which the function f is discontinuous.
	17.	For a short period of time during a sudden increase in exertion, a person’s heart rate, H, in beats per minute, is modelled by , where t is time, measured in seconds. a)  Determine H(0), and interpret the result. b) Determine the instantaneous rate of change of heart rate 5 seconds after the sudden increase in exertion. Explain what the result means.