Consider the sequence . Graph this sequence and use your graph to help you answer the following questions.

  1. Is the sequence bounded above by a function? If it is, enter the function of the variable that provides the “best” and “most obvious” upper bound; otherwise, enter DNE for does not exist.
  2. What is the limit of the function from part (a) as ? Enter a number, or enter DNE.
  3. Is the sequence bounded below by a function? If it is, enter the function of the variable that provides the “best” and “most obvious” lower bound; otherwise, enter DNE for does not exist.
  4. What is the limit of the function from part (c) as ? Enter a number, or enter DNE.
  5. Is the sequence bounded above by a number? Enter a number or enter DNE.
  6. Is the sequence bounded below by a number? Enter a number or enter DNE.
  7. Select all that apply: The sequence is




The sequence is





  1. The sequence is .
  2. The limit of the sequence is . Enter a number or DNE.
  1. When you first look at the sequence , you expect it to



  2. When you first look at the sequence , you expect it to



  3. If a sequence is alternating, it converge.