In Exercises 61-66, you will further explore finding deltas graphically. Use a CAS to pe...

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.