Functions and Limits Quiz
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Questions and Answers

What is the difference between a removable and non-removable discontinuity?

  • A removable discontinuity occurs when the function approaches a finite limit from both sides, while a non-removable discontinuity occurs when the function approaches different limits from both sides
  • A removable discontinuity is always a vertical asymptote, while a non-removable discontinuity can be a hole or jump
  • A removable discontinuity can be fixed by redefining the function at the point of discontinuity, while a non-removable discontinuity cannot (correct)
  • A removable discontinuity is always a hole in the graph of the function, while a non-removable discontinuity can be a jump or infinite oscillation

    • Which of the following statements is true about the limit of a function?

  • The limit of a function does not exist if the function is not continuous at that point (correct)
  • The limit of a function always exists if the function is continuous at that point
  • The limit of a function is always equal to infinity at a vertical asymptote
  • The limit of a function and the value of the function at that point are always the same

    • Which of the following is true about one-sided limits?

  • A one-sided limit does not exist if the function approaches different values from both sides
  • A one-sided limit always equals the two-sided limit
  • A one-sided limit exists if the function approaches the same value from both sides (correct)
  • A one-sided limit exists if the function approaches infinity from both sides

    • Flashcards

    Removable Discontinuity

    A removable discontinuity can be 'fixed' by changing the function's value at the point of discontinuity. Think of it like patching a hole in a road.

    Non-removable Discontinuity

    A non-removable discontinuity cannot be fixed by simply changing the function's value at the point of discontinuity.

    One-Sided Limit

    A one-sided limit exists if the function approaches the same value from both the left and the right sides of the point.

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