In Exercise you will further explore finding deltas graphically. Use a CAS to perform the following steps:
a. Plot the function near the point 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 graph the banding lines
and
together with the function ƒ near
d. From your graph in part (c), estimate a such that for all x
Test your estimate by plotting and over the interval
For your viewing window use
If any function values lie outside the interval
your choice of δ was too large. Try again with a smaller estimate.
e. Repeat parts (c) and (d) successively for and 0.001.
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