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means: For all € > 0) there is a > 0) such that for all x satisfying 0 < x-c| < 6 we have that |f(x) - L| < E. What if the limit does not equal L? Think about what the means in €, & language. Consider the following phrases: 1. € > 0) 2.8 > 0 3.0< x-c| < 6 4. f(x) - L > € 5. but lim f(x) = L x→c 6. such that for all 7. there is some 8. there is some x such that Order these statements so that they form a rigorous assertion that lim f(x) + L and enter their reference numbers in the appropriate sequence in these boxes: 3 2 7 4 6 5 8

means: For all € > 0) there is a > 0) such that for all x satisfying 0 < x-c| < 6 we have that |f(x) - L| < E. What if the limit does not equal L? Think about what the means in €, & language. Consider the following phrases: 1. € > 0) 2.8 > 0 3.0< x-c| < 6 4. f(x) - L > € 5. but lim f(x) = L x→c 6. such that for all 7. there is some 8. there is some x such that Order these statements so that they form a rigorous assertion that lim f(x) + L and enter their reference numbers in the appropriate sequence in these boxes: 3 2 7 4 6 5 8

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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means: For all € > 0) there is a > 0 such that for all x satisfying 0 < x-c| < 6 we have that |f(x) - L| < €. What if the limit does not equal L? Think about what the means in €, & language. Consider the following phrases: 1. € > 0 2.8 > 0 3.0< x-c| < 8 4. f(x) - LI > € 5. but 6. such that for all 7. there is some 8. there is some x such that lim f(x) = L x→c Order these statements so that they form a rigorous assertion that lim f(x) # L X C and enter their reference numbers in the appropriate sequence in these boxes: 327 4 5 8 3
Transcribed Image Text:means: For all € > 0) there is a > 0 such that for all x satisfying 0 < x-c| < 6 we have that |f(x) - L| < €. What if the limit does not equal L? Think about what the means in €, & language. Consider the following phrases: 1. € > 0 2.8 > 0 3.0< x-c| < 8 4. f(x) - LI > € 5. but 6. such that for all 7. there is some 8. there is some x such that lim f(x) = L x→c Order these statements so that they form a rigorous assertion that lim f(x) # L X C and enter their reference numbers in the appropriate sequence in these boxes: 327 4 5 8 3
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