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All statements below are false. Provide a counterexample of f and g each. (a) If f + g and fg are continuous, then f and g are continuous. (b) Iff is continuous, then f is continuous. (c) Suppose that f and g are continuous on R. (i) If f(x) > g(x) for all x > 0, then f(0) > g(0). (ii) If f(x) ≤ g(x) for all x, and g is never 0, then f/g is bounded.

All statements below are false. Provide a counterexample of f and g each. (a) If f + g and fg are continuous, then f and g are continuous. (b) Iff is continuous, then f is continuous. (c) Suppose that f and g are continuous on R. (i) If f(x) > g(x) for all x > 0, then f(0) > g(0). (ii) If f(x) ≤ g(x) for all x, and g is never 0, then f/g is bounded.

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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All statements below are false. Provide a counterexample of f and 9 each. (a) If f + g and fg are continuous, then f and g are continuous. (b) Iff is continuous, then f is continuous. (c) Suppose that f and g are continuous on R. (i) If f(x) > g(x) for all x > 0, then f(0) > g(0). (ii) If f(x) ≤ g(x) for all x, and g is never 0, then f/g is bounded.
Transcribed Image Text:All statements below are false. Provide a counterexample of f and 9 each. (a) If f + g and fg are continuous, then f and g are continuous. (b) Iff is continuous, then f is continuous. (c) Suppose that f and g are continuous on R. (i) If f(x) > g(x) for all x > 0, then f(0) > g(0). (ii) If f(x) ≤ g(x) for all x, and g is never 0, then f/g is bounded.
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