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Chapter 1: Q. 8 (page 135)
Write the constant multiple rule for limits in terms of delta鈥揺psilon statements.
For all , there exists such that if . Then,
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whererole="math" localid="1648190955831" .
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Explain why the Intermediate Value Theorem allows us to say that a function can change sign only at discontinuities and zeroes.
For each of the following sign charts, sketch the graph of a function f that has the indicated signs, zeros, and discontinuities:
Sketch a labeled graph of a function that satisfies the hypothesis of the Intermediate Value Theorem, and illustrate on your graph that the conclusion of the Intermediate Value Theorem follows.
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 satisfies the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem follows.
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