1.6.365 AP Calculus Exam Limits

In summary, the conversation discusses different limits and continuity of a function f(x). The main topic is determining which statements are true or false based on the given information. It is mentioned that a limit does not exist if the left and right-hand limits are not equal. The correct answer for statement c is that it is false, while all other statements (a, b, d, and e) are true. The conversation also mentions the importance of looking at both left and right-hand limits when determining continuity.
  • #1
karush
Gold Member
MHB
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ok I chose c being false, since a limit does not exist if f(x) is different coming from $\pm$
 
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  • #2
You need to look at left-hand and right-hand limits. I don't see where "$\pm$" comes into it.
 
  • #3
I believe that "from the left and from the right" was what Karush meant by "[tex]\pm[/tex]!

Yes, Karush, "c" is the only one that is false.

a) [tex]\lim_{x\to 2} f(x)[/tex] exists.
True. The limit is 2. (f(2)= 1 so f is NOT continuous there.)

b) [tex]\lim_{x\to 3} f(x)[/tex] exists.
True. The limit is 5. (Further f(3)= 5 so f is continuous there.)

c) [tex]\lim_{x\to 4} f(x)[/tex] exists.
False. The "limit from the left", [tex]\lim_{x\to 4^-} f(x)[/tex], is 2 while the "limit from the right", [tex]\lim_{x\to 4^+} f(x)[/tex], is 4. Since the two one-sided limits are not the same the limit itself does not exist.

d) [tex]\lim_{x\to 5} f(x)[/tex] exists.
True. The limit is 6. (Further f(5)= 6 so f is continuous there.)

e) f is continuous at x= 3.
True. As I said in (b), [tex]\lim_{x\to 3} f(x)[/tex] and f(3) both exist and are equal.
 
  • #4
ok I think the big visual hint on this one was the obvious disconnected gap.

mahalo everyone the comments really increase the insight on these.
 

1. What is the format of the 1.6.365 AP Calculus Exam Limits?

The 1.6.365 AP Calculus Exam Limits consists of a total of 45 multiple-choice questions and 6 free-response questions.

2. How much time is given to complete the 1.6.365 AP Calculus Exam Limits?

Students are given a total of 3 hours and 15 minutes to complete the exam. This includes a 10-minute break after the first section.

3. What topics are covered in the 1.6.365 AP Calculus Exam Limits?

The exam covers limits, continuity, derivatives, and integrals, as well as their applications in various contexts.

4. Can a calculator be used on the 1.6.365 AP Calculus Exam Limits?

Yes, a graphing calculator is allowed on the exam. However, there are certain restrictions on the types of functions and programs that can be used.

5. How is the 1.6.365 AP Calculus Exam Limits scored?

The multiple-choice section is scored based on the number of correct answers, with no penalty for incorrect answers. The free-response questions are scored on a rubric, with partial credit given for incomplete or incorrect solutions.

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