Limits and the Principle of Limits Quiz
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Questions and Answers

Which of the following is the correct definition of a limit of a function?

  • The value of the function at a specific number
  • The value that the function approaches as x approaches negative infinity
  • The value that the function approaches as x approaches a specific number (correct)
  • The value that the function approaches as x approaches infinity

    • In evaluating the limit of a function, we are concerned with the values of x in an open interval containing a but not a itself. Why is this important?

  • The limit is only defined for values of x less than a
  • The limit is only defined for values of x greater than a
  • The limit is always equal to the value of the function at a
  • The limit is undefined if a is included in the interval (correct)

    • Which of the following is a possible case when evaluating the limit of a function?

  • f(a) exists and f(a) = L
  • f(a) is undefined
  • f(a) exists, but f(a) ≠ L
  • All of the above (correct)

    • What is the limit of the function $f(x) = x + 3$ as x approaches 3?

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    What is the limit of the function $g(x) = \frac{x^2-9}{x-3}$ as x approaches 3?

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