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Chapter 1: Q 9. (page 107)
Write each of the inequalities in interval notation:
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State what it means for a functionf to be continuous at a point x = c, in terms of the delta–epsilon definition of limit.
Write a delta–epsilon proof that proves that f is continuous on its domain. In each case, you will need to assume that δ is less than or equal to 1.
Sketch a labeled graph of a function that satisfies the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem follows.
For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.
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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