Part CCSIR NET December 2024a-travelling-bump-of-constant-height

A travelling bump of constant height

For each positive integer n, define $f_{n} : [0, 1] \to R$ by $f_{n} (x) =$ nx $(1 - x)^{n}$ . Which of the following statements are true?

A. $(f_{n})_{n} \geq_{1}$ does not converge pointwise on [0, 1].
B. $(f_{n})_{n} \geq_{1}$ converges pointwise to a continuous function on [0, 1].✓
C. $(f_{n})_{n} \geq_{1}$ converges pointwise to a discontinuous function on [0, 1].
D. $(f_{n})_{n} \geq_{1}$ does not converge uniformly on [0, 1].✓

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.

50 are analysed free — try those first.

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