Part CCSIR NET December 2024periodic-plus-continuous-gives-uniform

Periodic plus continuous gives uniform

Let $f : R \to R$ be a continuous function such that f(x) = 0 for all x ≤ 0 and for all x ≥ 1. Define $F (x) = \sum (n = - \infty..\infty) f (x + n), x \in R$ . Which of the following statements are true?

A.F is bounded.✓
B.F is continuous on $R$ .✓
C.F is uniformly continuous on $R$ .✓
D.F is not uniformly continuous on $R$ .

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: Continuous on a bounded interval ⇒ bounded

Periodic plus continuous gives uniform

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