Chapter 1: Q. 54 (page 88)
Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits.
Short Answer
The value of and graph is

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Chapter 1: Q. 54 (page 88)
Sketch graphs by hand and use them to make approximations for each of the limits in Exercises 53–66. If a two-sided limit does not exist, describe the one-sided limits.
The value of and graph is

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Sketch the graph of a function f described in Exercises 27–32, if possible. If it is not possible, explain why not.
f is left continuous at x = 1 and right continuous at x = 1, but is not continuous at x = 1, and f(1) = −2.
For each limit statement, use algebra to find δ or N in terms of or M, according to the appropriate formal limit definition.
find δ in terms of .
For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.
Write delta-epsilon proofs for each of the limit statements in Exercises .
.
For each limit statement in Exercises , use algebra to find or in terms of or , according to the appropriate formal limit definition.
,findin terms of.
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