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Chapter 1: Q. 26 (page 107)
Use algebra to find the largest possible value of δ or smallest possible value of N that makes each implication is true. Then verify and support your answers with labeled graphs.
If, then.
The required value of N is .
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Write delta-epsilon proofs for each of the limit statements in Exercises .
.
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 in Exercises 43–54, use graphs and algebra to approximate the largest value of such that if localid="1648023101818"
localid="1648023199049" role="math"
Write a delta–epsilon proof that proves that f is continuous on its domain. In each case, you will need to assume that δ is less than or equal to 1.
For each limit statement in Exercises , use algebra to find or in terms of or , according to the appropriate formal limit definition.
, findin terms of.
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