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Chapter 1: Q. 12 (page 148)
Describe in terms of large and small numbers why it makes intuitive sense that limits of the form (a)(b)must equal 0.
(a)and the number is small.
(b)and the number is small.
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Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem does not necessarily hold.
For each limit in Exercises 43–54, use graphs and algebra to approximate the largest value of such that if localid="1648023101818"
localid="1648023199049" role="math"
State what it means for a function f to be left continuous at a point x = c, in terms of the delta–epsilon definition of limit.
Calculate each of the limits:
.
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| < .
.
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