Consider the following statements: (i) There exists a function f: R → R which is discontinuous at 1,1/2,1/3,1/4,... but is continuous at every other point. (ii) There exists a function f:R→R which is discontinuous at 1, 1/2, 1/3, 1/4,... and at 0 but is continuous at every other point. Which statements are true? O Only statement (i) is true. Both statements are true. Only statement (ii) is true. O Neither statement is true

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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QUESTION 3
Consider the following statements:
(i) There exists a function f: R → R which is discontinuous at 1,1/2,1/3,1/4,... but is continuous at every other point.
(ii) There exists a function f:R→R which is discontinuous at 1, 1/2, 1/3, 1/4,... and at 0 but is continuous at every other point.
Which statements are true?
O Only statement (i) is true.
O Both statements are true.
O Only statement (ii) is true.
O Neither statement is true
Transcribed Image Text:QUESTION 3 Consider the following statements: (i) There exists a function f: R → R which is discontinuous at 1,1/2,1/3,1/4,... but is continuous at every other point. (ii) There exists a function f:R→R which is discontinuous at 1, 1/2, 1/3, 1/4,... and at 0 but is continuous at every other point. Which statements are true? O Only statement (i) is true. O Both statements are true. O Only statement (ii) is true. O Neither statement is true
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