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Chapter 1: Q. 12 (page 153)
Limits of basic functions: Fill in the blanks to complete the limit rules that follow. You may assume that is positive
=?.
The value of the limit.
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For each limit statement , use algebra to find δ > 0 in terms of > 0 so that if 0 < |x − c| < δ, then | f(x) − L| < .
For each limit statement , use algebra to find δ > 0 in terms of > 0 so that if 0 < |x − c| < δ, then | f(x) − L| < .
.
Write delta-epsilon proofs for each of the limit statements in Exercises .
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For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.
In Exercises 39–44, use Theorem 1.16 and left and right limits to determine whether each function f is continuous at its break point(s). For each discontinuity of f, describe the type of discontinuity and any one-sided discontinuity.
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