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Questions and Answers
Which of the following statements about the limits of the function f(x) as x approaches 0 is true?
Which of the following statements about the limits of the function f(x) as x approaches 0 is true?
- c. The limit of f(x) as x approaches 0 from the left does not exist, the limit as x approaches 0 from the right does not exist, and the limit as x approaches 0 does not exist.
- d. The limit of f(x) as x approaches 0 from the left is 1, the limit as x approaches 0 from the right is 0, and the limit as x approaches 0 does not exist.
- b. The limit of f(x) as x approaches 0 from the left is 1, the limit as x approaches 0 from the right is 0, and the limit as x approaches 0 exists and is equal to 1/2. (correct)
- a. The limit of f(x) as x approaches 0 from the left exists, the limit as x approaches 0 from the right exists, and the limit as x approaches 0 exists and is equal to 1/2.
Which of the following is true about the function f(x) as x approaches 0 from the left?
Which of the following is true about the function f(x) as x approaches 0 from the left?
- a. The function is continuous at x=0.
- b. The function has a removable discontinuity at x=0.
- d. The function has an infinite discontinuity at x=0.
- c. The function has a jump discontinuity at x=0. (correct)
Which of the following is true about the function f(x) as x approaches 0 from the right?
Which of the following is true about the function f(x) as x approaches 0 from the right?
- c. The function has a jump discontinuity at x=0.
- d. The function has an infinite discontinuity at x=0.
- a. The function is continuous at x=0. (correct)
- b. The function has a removable discontinuity at x=0.
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