# 1.6.365 AP Calculus Exam Limits

• MHB
• karush
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.
karush
Gold Member
MHB
ok I chose c being false, since a limit does not exist if f(x) is different coming from $\pm$

Last edited:
You need to look at left-hand and right-hand limits. I don't see where "$\pm$" comes into it.

I believe that "from the left and from the right" was what Karush meant by "$$\pm$$!

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

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

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

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

d) $$\lim_{x\to 5} f(x)$$ 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), $$\lim_{x\to 3} f(x)$$ and f(3) both exist and are equal.

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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