Find an example of a sequence of continuous functions {fn} defined on theinterval [0, 1] such that 0 < f(x) < 1,| fa(x) dxconverges to 0 as n → ∞, and that { fn(x)} does not converge at any point xin [0, 1].

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Find an example of a sequence of continuous functions {fn} defined on the interval [0, 1] such that 0 < fn(x) < 1, | fn(x) dx converges to 0 as n o, and that { fn(x)} does not converge at any point x in [0, 1].

Find an example of a sequence of continuous functions {fn} defined on the interval [0, 1] such that 0 < fn(x) < 1, | fn(x) dx converges to 0 as n o, and that { fn(x)} does not converge at any point x in [0, 1].

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter5: Graphs And The Derivative

Section5.3: Higher Derivatives, Concavity, And The Second Derivative Test

Problem 61E

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Question

Find an example of a sequence of continuous functions {fn} defined on the
interval [0, 1] such that 0 < f(x) < 1,
| fa(x) dx
converges to 0 as n → ∞, and that { fn(x)} does not converge at any point x
in [0, 1].

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