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Question 18 Suppose f: (0, 1)→ R is continuous and let (an) be a Cauchy sequence in (0, 1). Consider the following statements: (i) f((0, 1)) is open. (ii) (f (an)) is a Cauchy sequence. Which statements must be true? O Both statements must be true. O Statement (ii), but not statement (i), must be true. ONeither statement must be true. O Statement (i), but not statement (ii), must be true.

Question 18 Suppose f: (0, 1)→ R is continuous and let (an) be a Cauchy sequence in (0, 1). Consider the following statements: (i) f((0, 1)) is open. (ii) (f (an)) is a Cauchy sequence. Which statements must be true? O Both statements must be true. O Statement (ii), but not statement (i), must be true. ONeither statement must be true. O Statement (i), but not statement (ii), must be true.

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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Question 18 Suppose f: (0, 1)→ R is continuous and let (an) be a Cauchy sequence in (0, 1). Consider the following statements: (i) f((0, 1)) is open. (ii) (f (an)) is a Cauchy sequence. Which statements must be true? O Both statements must be true. O Statement (ii), but not statement (i), must be true. ONeither statement must be true. O Statement (i), but not statement (ii), must be true.
Transcribed Image Text:Question 18 Suppose f: (0, 1)→ R is continuous and let (an) be a Cauchy sequence in (0, 1). Consider the following statements: (i) f((0, 1)) is open. (ii) (f (an)) is a Cauchy sequence. Which statements must be true? O Both statements must be true. O Statement (ii), but not statement (i), must be true. ONeither statement must be true. O Statement (i), but not statement (ii), must be true.
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