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Chapter 1: Q. 34 (page 153)
Indeterminate forms: Identify which of the limit forms listed here are indeterminate. For each form that is not indeterminate, describe the behavior of a limit of that form.
The given limit form is an indeterminate form.
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Write each of the inequalities in interval notation:
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.
Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample.
(a) A limit exists if there is some real number that it is equal to.
(b) The limit of as is the value .
(c) The limit of as might exist even if the value of does not.
(d) The two-sided limit of as exists if and only if the left and right limits of exists as .
(e) If the graph of has a vertical asymptote at , then .
(f) If , then the graph of has a vertical asymptote at .
(g) If , then the graph of has a horizontal asymptote at .
(h) If, then the graph ofhas a horizontal asymptote at.
Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Intermediate Value Theorem, and illustrate on your graph that the conclusion of the Intermediate Value Theorem does not necessarily hold.
Use the delta-epsilon definition of continuity to argue that f is or is not continuous at the indicated point .
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