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Chapter 1: Q. 42 (page 149)
Calculate each limit in Exercises 35-80.
The limit of the expression is.
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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.
Write delta-epsilon proofs for each of the limit statements in Exercises .
.
Use the delta-epsilon definition of continuity to argue that f is or is not continuous at the indicated point .
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 limit in Exercises 33–38, either use continuity to calculate the limit or explain why Theorem 1.16 does not apply.
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