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3. Assume that f is uniformly continuous on a bounded set S, prove that f(S) is bounded. (hint: thm 19.4, 11.5) 4. Let ƒ(x) = (x-1)(x−3)² , ‚ determine limä→1 ƒ (x), limx→2 ƒ (x), limx→3 ƒ (x). (hint: limit may be infinite or does not exist).

3. Assume that f is uniformly continuous on a bounded set S, prove that f(S) is bounded. (hint: thm 19.4, 11.5) 4. Let ƒ(x) = (x-1)(x−3)² , ‚ determine limä→1 ƒ (x), limx→2 ƒ (x), limx→3 ƒ (x). (hint: limit may be infinite or does not exist).

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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3. Assume that ƒ is uniformly continuous on a bounded set S, prove that f(S) is bounded. (hint: thm 19.4, 11.5) 4. Let f(x) = (x-1)(x-3)2, determine limx→1 ƒ(x), limx→2 ƒ (x), limx→3 ƒ(x). (hint: limit may be infinite or does not exist).
Transcribed Image Text:3. Assume that ƒ is uniformly continuous on a bounded set S, prove that f(S) is bounded. (hint: thm 19.4, 11.5) 4. Let f(x) = (x-1)(x-3)2, determine limx→1 ƒ(x), limx→2 ƒ (x), limx→3 ƒ(x). (hint: limit may be infinite or does not exist).
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