Calculate each of the limits in Exercises 15–20 (a) using
L’Hopital’s rule and (b) without using L’H ˆ opital’s rule.
we have been given,
Sketch careful, labeled graphs of each function f in Exercises 63–82 by hand, without consulting a calculator or graphing utility. As part of your work, make sign charts for the signs, roots, and undefined points of and examine any relevant limits so that you can describe all key points and behaviors of f.
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