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Prove the following theorem. Theorem: “Squeeze theorem" for infinite limits Let a e R. Let f and g be two functions defined at least on an interval around a, except possibly at a. IF • f(x) > g(x) for all æ in some interval around a, except possibly a lim g(x) = ∞, THEN lim f(r) = 0.

Prove the following theorem. Theorem: “Squeeze theorem" for infinite limits Let a e R. Let f and g be two functions defined at least on an interval around a, except possibly at a. IF • f(x) > g(x) for all æ in some interval around a, except possibly a lim g(x) = ∞, THEN lim f(r) = 0.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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(5) The Squeeze theorem says that if f, g, and h are three functions satisfying f(x) < g(x) < h(x) for all r near some real number a, and lim,-»a f(x) = lim,→a h(x), then g is forced (or "squeezed") to go to the same place (and therefore to have the same limit). This question is a variation on that idea, inspired by students often asking whether the Squeeze theorem is true for infinite limits. Prove the following theorem. Theorem: “Squeeze theorem" for infinite limits Let a e R. Let f and g be two functions defined at least on an interval around a, except possibly at a. IF • f(2) > g(x) for all r in some interval around a, except possibly a lim g(x) = 0, THEN lim f(r) = 00.
Transcribed Image Text:(5) The Squeeze theorem says that if f, g, and h are three functions satisfying f(x) < g(x) < h(x) for all r near some real number a, and lim,-»a f(x) = lim,→a h(x), then g is forced (or "squeezed") to go to the same place (and therefore to have the same limit). This question is a variation on that idea, inspired by students often asking whether the Squeeze theorem is true for infinite limits. Prove the following theorem. Theorem: “Squeeze theorem" for infinite limits Let a e R. Let f and g be two functions defined at least on an interval around a, except possibly at a. IF • f(2) > g(x) for all r in some interval around a, except possibly a lim g(x) = 0, THEN lim f(r) = 00.
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