AP Calculus BC Unit 1 — Limits and Continuity Practice Test
AP Calculus BC Unit 1 — Limits and Continuity Practice Test
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Question 1 of 19
1. Question
Which of the following functions have the same instantaneous rate of change when x=1 and x=2 ?
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Question 2 of 19
2. Question
At which point does the function have an approximate instantaneous rate of change of 0?
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Question 3 of 19
3. Question
Which of the following functions has an instantaneous rate of change of approximately 2 when x=1 ?
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Question 4 of 19
4. Question
Where is the following function discontinuous?
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Question 5 of 19
5. Question
For what x value does the instantaneous rate of change of f ( x ) not exist above?
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Question 6 of 19
6. Question
Given the graph of above, what is
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Question 7 of 19
7. Question
For the piecewise function:
,
find .
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Question 8 of 19
8. Question
Given the above graph of , what is
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Question 9 of 19
9. Question
The function is defined over the real numbers. This table gives a few values of .
What is a reasonable estimate for ?
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Question 10 of 19
10. Question
Functions and are graphed. Find .
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Question 11 of 19
11. Question
Functions and are graphed. Find .
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Question 12 of 19
12. Question
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Question 13 of 19
13. Question
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Question 14 of 19
14. Question
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Question 15 of 19
15. Question
We want to find . Direct substitution and other algebraic methods don’t seem to work. Looking at the graph of , we can estimate that the limit is equal to 1.
To prove that , we can use the squeeze theorem. Madison suggested that we use the functions and in order to apply the squeeze theorem. Does Madison’s suggestion seem to be correct?
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Question 16 of 19
16. Question
Which of the following functions are continuous for all real numbers?
g ( x ) =2^{ x}
f ( x )=ln ( x )
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Question 17 of 19
17. Question
Consider graphs A, B, and C. The dashed lines represent asymptotes. Which graphs agree with this statement? Choose all answers that apply.
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Question 18 of 19
18. Question
Let h be a continuous function on the closed interval [0,4], where h ( 4 )=− 2 . h ( 0 )=2 and Which of the following is guaranteed by the Intermediate Value Theorem?
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Question 19 of 19
19. Question
Anastasia’s teacher gave her a flow chart (below) and asked her to find for . Which shows Anastasia’s easiest path to finding the limit?
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