Chapter 1: Q. 48 (page 88)
Use tables of values to make educated guesses for each of the limits in Exercises 39–52.
Short Answer
The value of the limit
Chapter 1: Q. 48 (page 88)
Use tables of values to make educated guesses for each of the limits in Exercises 39–52.
The value of the limit
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Get started for freeFor each limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.
State what it means for a function f to be right continuous at a point x = c, in terms of the delta–epsilon definition of limit.
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.
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.
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 .
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