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 L Epsilon Delta

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.

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.

Question 4 Do you think it would be possible to find such a value of delta graphically 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.

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.