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Chapter 1: Q. 34 (page 107)
For each limit statement , use algebra to find 未 > 0 in terms of > 0 so that if 0 < |x 鈭� c| < 未, then | f(x) 鈭� L| < .
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Use what you know about one-sided limits to prove that a function is continuous at a point if and only if it is both left and right continuous at .
Calculate each of the limits:
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In Exercises 39鈥�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.
Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem does not necessarily hold.
Write delta-epsilon proofs for each of the limit statements in Exercises .
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