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Chapter 1: Q. 7 (page 137)
Calculate the derivative of at . At some point you should need the characterization of e given in Theorem 1.26.
The derivative is .
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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.
For each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.
Write delta-epsilon proofs for each of the limit statements in Exercises
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.
Calculate each of the limits:
.
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