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Chapter 1: Q. 3 (page 107)
Write down the formal delta-epsilon statement you would have to prove in order to prove the limit statement.
For all epsilon positive there exists a delta positive if
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Calculate each of the limits:
.
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.
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| < .
Sketch the graph of a function f described in Exercises 27–32, if possible. If it is not possible, explain why not.
f is left continuous at x = 2 but not continuous at x = 2, and f(2) = 3.
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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