Physics · Real Analysis
Let fn(x) = (2x)n, x ∈ [0, 12] and n ∈ ℕ be a sequence of functions; then _________.
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1{fn(x)}n ∈ ℕ converges pointwise to f(x), where f(x) = 1 for all x ∈ [0, 12].
- 2{fn(x)}n ∈ ℕ does not converge uniformly on [0, 12].✓
- 3{fn(x)}n ∈ ℕ converges pointwise to f(x), where f(x) = 0 for all x ∈ [0, 12].
- 4{fn(x)}n ∈ ℕ converges uniformly on [0, 12].
Correct answer
{fn(x)}n ∈ ℕ does not converge uniformly on [0, 12].
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