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Chapter 1: Q 7. (page 107)
Write each of the inequalities in interval notation:
Answer is
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Each function in Exercises 9鈥�12 is discontinuous at some value x = c. Describe the type of discontinuity and any one-sided continuity at x = c, and sketch a possible graph of f.
Sketch the graph of a function f described in Exercises 27鈥�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) = 鈭�2.
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.
Calculate each of the limits:
.
For each limit statement, use algebra to find 未 or N in terms of or M, according to the appropriate formal limit definition.
find 未 in terms of .
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