AP Calculus AB: 1.1 Introducing Calculus: Can Change Occur at an Instant? – Exam Style questions with Answer- MCQ

Question

 The graph of the function f is shown in the figure above. Which of the following statements about
f is true?

(A)\(\lim_{x\rightarrow a}f(x)=\lim_{x\rightarrow b}f(x)\)
(B)\(\lim_{x\rightarrow a}f(x)=2\)
(C)\(\lim_{x\rightarrow b}f(x)=2\)
(D)\(\lim_{x\rightarrow a}f(x)=1\)
(E)\(\lim_{x\rightarrow a}f(x)\) does not exit

▶️Answer/Explanation

Ans:B 

Statement B is true because  . \(\lim_{x\rightarrow a^-}f(x)=2=\lim_{x\rightarrow a^+}f(x)\).Also \(\lim_{x\rightarrow b}f(x)\) does not exist because the left- and right-sided limits are not equal, so neither (A), (C), nor (D) are true.

Question

The position of a particle moving to the right on the x -axis is given by x(t) , where x(t) is measured in centimeters and  t is measured in seconds for  0≤t≤50 . If y=x(t) is a linear function, which of the following would most likely give the best estimate of the speed of the particle, in centimeters per second, at time  t=10  seconds?

A x(10)

B  \(\frac{x(10)}{10}\)

C x(11)-x(9)

D The slope of the graph of y=x(t)

▶️Answer/Explanation

Ans:D

This gives the exact value of the speed of the particle at any time t  in the interval [0,50]

Question

A model rocket leaves the ground at time t=0 and travels straight up from the ground. The height, in feet, of the rocket above the ground is given by  y(t), where t is measured in seconds for 0≤t≤120 .Values of y(t) for selected values of t are given in the table above. Of the following values of  t,at which value would the velocity of the rocket most likely be greatest based on the data in the table?
A t=20
B t=40
C t=60
D t=80

▶️Answer/Explanation

Ans:D
Considering the four values of t in the options and the differences between successive values of y(t) in the table, note that the differences are increasing, with  y(80)−y(60) being the greatest difference. Therefore, the velocity of the rocket appears to be increasing ast increases, and so the greatest velocity would occur at the greatest of the four

Question

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 given above. Which of the following is the best estimate for the speed of the particle at time

t=4

 ?

A 0

B 5

C \(\frac{20}{3}\)

D 20

▶️Answer/Explanation

Ans:A

At time

t=4

, the particle is stationary at the position x

(t)=20

.

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