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The sequential characterization of limits states that the following are equivalent 1) lim f(x)=L 2) For every sequence {n}, with the properties that lim za and za for any n E N, we have that the sequence {f(z)) has the property lim f(x)=L. Assume that {} is a sequence where →a and a for any n. Which of the following statements are true? Select all correct expressions. If lim g(x)= M then the lim g() exists 2-0 Olim sin (+/-) = sin (lim = sin(lim+). Let {} be a sequence where y → a and Una for any n. If lim f(x) lim (3) then lim f(z) does not exist. □ If lim f(x)= L then lim, f(x) = L None of the above

The sequential characterization of limits states that the following are equivalent 1) lim f(x)=L 2) For every sequence {n}, with the properties that lim za and za for any n E N, we have that the sequence {f(z)) has the property lim f(x)=L. Assume that {} is a sequence where →a and a for any n. Which of the following statements are true? Select all correct expressions. If lim g(x)= M then the lim g() exists 2-0 Olim sin (+/-) = sin (lim = sin(lim+). Let {} be a sequence where y → a and Una for any n. If lim f(x) lim (3) then lim f(z) does not exist. □ If lim f(x)= L then lim, f(x) = L None of the above

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The sequential characterization of limits states that the following are equivalent 1) lim f(x) = L 2) For every sequence {}, with the properties that lim za and za for any nEN, we have that the sequence {f(x)} has the property lim f(x) = L. 14-900 Assume that {} is a sequence where →a and 2 a for any n. Which of the following statements are true? Select all correct expressions. If lim g(x) = M then the lim g() exists 1 Olim sin a ( ² + ²/²) = sin ( lim² = 1 + 2/2 ). 11-900 n² Let {v} be a sequence where y → a and Una for any n. If lim f(x) 11-100 then lim f(z) does not exist. lim f(3) 11-100 If lim f(x) = L then lim, f(x)=L -HE None of the above
Transcribed Image Text:The sequential characterization of limits states that the following are equivalent 1) lim f(x) = L 2) For every sequence {}, with the properties that lim za and za for any nEN, we have that the sequence {f(x)} has the property lim f(x) = L. 14-900 Assume that {} is a sequence where →a and 2 a for any n. Which of the following statements are true? Select all correct expressions. If lim g(x) = M then the lim g() exists 1 Olim sin a ( ² + ²/²) = sin ( lim² = 1 + 2/2 ). 11-900 n² Let {v} be a sequence where y → a and Una for any n. If lim f(x) 11-100 then lim f(z) does not exist. lim f(3) 11-100 If lim f(x) = L then lim, f(x)=L -HE None of the above
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