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Delta, Epsilon, and Limits

Delta, Epsilon, and Limits. Question 1. What is the largest value you found for delta for this value or epsilon? Record the values of C, L, epsilon, delta and in a table on a separate sheet of paper . C - 2 -1 L - 5.4 -3.9 Epsilon - .2 .128

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Delta, Epsilon, and Limits

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  1. Delta, Epsilon, and Limits

  2. Question 1 • What is the largest value you found for delta for this value or epsilon? Record the values of C, L, epsilon, delta and in a table on a separate sheet of paper. C - 2 -1 L - 5.4 -3.9 Epsilon - .2 .128 Delta - .03884 .0927

  3. Question 2 • When you set epsilon to half its previous value, did your value for delta reduce by half as well? Try other fractions of E, such as 2/3 or 2/5 • Delta became .0194, so yes it reduced in half.

  4. Question 3 • Was it possible in each case to set a value of delta that satisfied the definition of a limit? What can you conclude about the function as x approaches C in each case? • Yes, as long as delta is adjusted so that it is within epsilon. As x approaches C, f(x) is getting closer and closer to the limit.

  5. Question 4 • Do you think it would be possible to find such a value of deltagraphically for every possible value of C and epsilon? If not, what values of C and E would not work? • Yes, since quadratic equations are continuous.

  6. Question 5 • Was it possible in each case to set a value of delta that satisfies the definition of a limit? If not, note the values of C, L, and epsilon for which it was not possible. Did your effort fail because L does not exist, or because does not exist, or because you could not adjust delta correctly? What can you conclude about the function as x approaches C? • Yes, since the equations used were quadratic and thus always continuous. As x approaches C, f(x) is getting closer to the limit.

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