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# Limits of Sequences & Functions Chapter Exam

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### Page 1

#### Question 1 1. How many discontinuities are in the function f(x), where f(x) = -1 when x < -1, and f(x) = x for values of x ≥ -1?

####
Question 2
2.
Which of the following functions are discontinuous?

I) f(x) = x^2 + 1 when x < 0 and f(x) = x + 1 when x ≥ 0

II) f(x) = x when x < 0, f(x) = 1 when x = 0, and f(x) = -x when x > 0

III) f(x) = 2

#### Question 3 3. How do you write the limit of the function g(k) as the variable k approaches the constant C?

#### Question 4 4. Which of the following is true?

#### Question 5 5. Evaluate the limit below.

### Page 2

#### Question 6 6. Evaluate the limit below.

#### Question 7 7. Use the given graph and formula to solve for z.

#### Question 8 8. Use the given formula to solve for z

#### Question 9 9. Use the graph to solve for z.

#### Question 10 10. If g(k) is continuous everywhere, then which of the following is true?

### Page 3

#### Question 11 11. What are the regions of continuity given the following?

#### Question 12 12. Which of the following functions is continuous for every value of x except x=0?

#### Question 13 13. What type of discontinuity is in the graph of f(x) = {2 for x < 0; (x + 2) for x ≥ 0}?

#### Question 14 14. What type of discontinuity is in the graph of f(x) = 1/(x+2)?

####
Question 15
15.
Assume a function *f*(*x*), which is continuous over the range [-4, 5], such that *f*(-4) = -3 and *f*(5) = 8. Which of the following statements is true?

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####
Question 16
16.
Suppose a function *f*(*x*) is continuous over the interval [-2, 8]. Which of the following is true?

#### Question 17 17. Consider the function below. According to the intermediate value theorem, is there a solution to f(x) = 0 for a value of x between -5 and 5?

#### Question 18 18. Consider the function f(x) below. Considering the intermediate value theorem and the vertical asymptote at x=0, is the following statement true or false? For any number C greater than 0, there is a positive value of x that satisfies the equation f(x)=C.

#### Question 19 19. Using the squeeze theorem, what is z?

#### Question 20 20. Using the squeeze theorem, what is z?

### Page 5

#### Question 21 21. The limit of sin(x) as x approaches a value will always be:

#### Question 22 22. The limit of f(x) = x^2 * log (x) when x > 0 is 0 for how many values of x?

#### Question 23 23. I have a function where f(1) = 0 and f(4) = 3. Why might there not be an x between 1 and 4 such that f(x) = 1?

#### Question 24 24. If all we know about the following functions is that they're continuous, and the given values, then which will have a solution for f(x) = 2?

#### Question 25 25. How many discontinuities are in this function?

### Page 6

#### Question 26 26. Use the graph to solve for z.

#### Question 27 27. The expression below can also be written as:

#### Question 28 28. Solve for the limit:

#### Question 29 29. How do you write the limit of f(x) as x goes to zero from the left?

#### Question 30 30. What are the regions of continuity for y defined as?

#### Limits of Sequences & Functions Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!