In Exercises 61-66, you will further explore finding deltas graphically. Use a CAS to perform the following steps:
a. Plot the function y = f(x) near the point x0 being approached.
b. Guess the value of the limit L and then evaluate the limit symbolically to see if you guessed correctly.
c. Using the value = 0.2, graph the banding lines
and y2 = L +
together with the function f near x0.
d. From your graph in part (c), estimate δ > 0 such that for all x
Test your estimate by plotting f, y1, and y2 over the interval For your viewing window use
If any function values lie outside the interval
your choice of δ as too large. Try again with a smaller estimate.
e. Repeat parts (c) and (d) successively for = 0.1, 0.05, and 0.001.
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