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Chapter 1: Q. 21 (page 153)
Limits of combinations: Fill in the blanks to complete the limit
rules that follow. You may assume that k and c are any real
numbers and that both exist.
The value of the limit is
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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| < .
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.
Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Intermediate Value Theorem, and illustrate on your graph that the conclusion of the Intermediate Value Theorem does not necessarily hold.
Explain why the Intermediate Value Theorem allows us to say that a function can change sign only at discontinuities and zeroes.
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