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Chapter 1: Q. 41 (page 136)
Calculate each of the limits in Exercises .
.
The value ofis,.
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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 = 1 and right continuous at x = 1, but is not continuous at x = 1, and f(1) = −2.
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| < .
For each functionf graphed in Exercises23–26, describe the intervals on whichf is continuous. For each discontinuity off, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements.
Write delta-epsilon proofs for each of the limit statements in Exercises .
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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.
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