Show by example that the following statement is wrong. The number L is the limit of f(x) as x approaches o if f(x) gets closer to L as x approaches c. Explain why the function in your example does not have the given value of L as a limit as x→c. Which of the following graphs shows a function that serves as an example that makes the statement wrong? OA. Ay Q O B. Ay с BREEEN Q Q OC. Explain why the function in your example does not have the given value of L as a limit as x→c. Choose the correct answer below. OA. Although f(x) gets closer to L as x approaches c, the function values are not symmetric, so lim f(x) * L. X-C OB. Although f(x) gets closer to L as x approaches c, for a small enough e > 0, there is no 8 such that 0
Show by example that the following statement is wrong. The number L is the limit of f(x) as x approaches o if f(x) gets closer to L as x approaches c. Explain why the function in your example does not have the given value of L as a limit as x→c. Which of the following graphs shows a function that serves as an example that makes the statement wrong? OA. Ay Q O B. Ay с BREEEN Q Q OC. Explain why the function in your example does not have the given value of L as a limit as x→c. Choose the correct answer below. OA. Although f(x) gets closer to L as x approaches c, the function values are not symmetric, so lim f(x) * L. X-C OB. Although f(x) gets closer to L as x approaches c, for a small enough e > 0, there is no 8 such that 0
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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Transcribed Image Text:Show by example that the following statement is wrong.
The number L is the limit of f(x) as x approaches o if f(x) gets closer to Las x approaches c.
Explain why the function in your example does not have the given value of L as a limit as x→c.
Which of the following graphs shows a function that serves as an example that makes the statement wrong?
O A.
Ay
O B.
CECCHI
Q
O C.
с
Explain why the function in your example does not have the given value of L as a limit as x→c. Choose the correct answer below.
O A. Although f(x) gets closer to L as x approaches c, the function values are not symmetric, so lim f(x) #L.
X-C
OB. Although f(x) gets closer to L as x approaches c, for a small enough e > 0, there is no 8 such that 0 < x-c/<8⇒ |f(x)-L/ < e.
OC. Although f(x) gets closer to Las x approaches c, f(c) # L.
O D. Although f(x) gets closer to Las x approaches c, the function oscillates too greatly, so lim f(x) # L.
X-C
O D.
Ay
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