AP Calculus Exam Practice I - Limits Focus (No Calculator)

• I only

• I and III only

• II and III only

• I, II, and III only

The size of a population of bacteria is modeled by the function P, where P(t) gives the number of bacteria and t gives the number of hours after midnight for 0 ≤ t ≤ 10. The graph of the function P and the line tangent to P at t = 8 are shown here. Which of the following gives the best estimate for the instantaneous rate of change of P at t = 8?

• P(8)

• The slope joining (0,P(0)) and (8,P(8))

• The slope joining (0,P(0)) and (10,P(10))

• The slope joining (7.9,P(7.9)) and (8.1,P(8.1))

A particle is moving on the x-axis and the position of the particle at time t is given by x(t), whose graph is shown above. Which of the following is the best estimate for the speed of the particle at time t=4 ?

• 0

• 5

• 10

A car is driven on a straight road, and the distance traveled by the car after time t=0 is given by a quadratic function s, where s(t) is measured in feet and t is measured in seconds for 0≤t≤12. Of the following, which gives the best estimate of the velocity of the car, in feet per second, at time t=6 seconds?

• s(6)

• 1/2

• 1

• 4

• DNE

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• 
• 
• 

• The value of the function f at x=3 is 5.

• The value of the function f at x=5 is 3.

• As x approaches 3, the values of f(x) approach 5.

• As x approaches 5, the values of f(x) approach 3.

The graphs of the functions f and g are shown in the figures above. Which of the following statements is false?

• II only

• III only

• I & II only

• II & III only

• I, II, & III

The table here gives values of the function f at selected values of x. Which of the following conclusions is supported by the data in the table?