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The limit at infinity lim f(x) = L means that for any e > 0, there exists N>0 such that f(x)-L N. X-00 Use the definition of a limit at infinity to prove the statement lim X→∞0 State the steps for proving that lim f(x)=L. X→∞0 4x + 5 X = 4 (CXX)

The limit at infinity lim f(x) = L means that for any e > 0, there exists N>0 such that f(x)-L N. X-00 Use the definition of a limit at infinity to prove the statement lim X→∞0 State the steps for proving that lim f(x)=L. X→∞0 4x + 5 X = 4 (CXX)

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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The limit at infinity lim f(x)= L means that for any e > 0, there exists N> 0 such that f(x)-L<e whenever x > N. X→∞0 Use the definition of a limit at infinity to prove the statement lim X-00 State the steps for proving that lim f(x)=L. X→∞0 Let e and N be arbitrary positive numbers. Use the inequality X> E Identify f(x). f(x) = 1 Identify L. L=1 4x + 5 X =4. f(x)-L>e to find a condition of the form f(x)-L<N, where L depends only on the value of N. and use the relationship between x and N to prove that x>e. ▬ 4 Review the second step for proving that lim f(x) = L. Use the given inequality and the desired form of the condition to determine a plausible expression for N. X→∞0 Q Search xxx) N=1 Review the final step for proving that lim f(x) = L. What operations, when performed on both sides of the assumed inequality, will prove the desired inequality after simplification? X-3 acer amazon Then, for any e > 0, assume 38888 Next 3:49 PM 3/22/2023
Transcribed Image Text:The limit at infinity lim f(x)= L means that for any e > 0, there exists N> 0 such that f(x)-L<e whenever x > N. X→∞0 Use the definition of a limit at infinity to prove the statement lim X-00 State the steps for proving that lim f(x)=L. X→∞0 Let e and N be arbitrary positive numbers. Use the inequality X> E Identify f(x). f(x) = 1 Identify L. L=1 4x + 5 X =4. f(x)-L>e to find a condition of the form f(x)-L<N, where L depends only on the value of N. and use the relationship between x and N to prove that x>e. ▬ 4 Review the second step for proving that lim f(x) = L. Use the given inequality and the desired form of the condition to determine a plausible expression for N. X→∞0 Q Search xxx) N=1 Review the final step for proving that lim f(x) = L. What operations, when performed on both sides of the assumed inequality, will prove the desired inequality after simplification? X-3 acer amazon Then, for any e > 0, assume 38888 Next 3:49 PM 3/22/2023
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