- Let f: [0,1] -> [0,00) be Lebesgue measurable. For n € N, define fr 9n 1 + fn (a) Explain why gn(t) dt exists and is finite for all n. (b) Prove that lim gn (t) dt exists and find an expression for it. Make sure to state which major Theorem are you using in your proof. 72-00

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Chapter2: Second-order Linear Odes
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2. Let f: [0, 1] ->>
[0,00) be Lebesgue measurable. For n € N, define
fn
In
1+ fn
gn(t) dt exists and is finite for all n.
(a) Explain why
(b) Prove that lim
72-00
major Theorem are you using in your proof.
gn (t) dt exists and find an expression for it. Make sure to state which
Transcribed Image Text:2. Let f: [0, 1] ->> [0,00) be Lebesgue measurable. For n € N, define fn In 1+ fn gn(t) dt exists and is finite for all n. (a) Explain why (b) Prove that lim 72-00 major Theorem are you using in your proof. gn (t) dt exists and find an expression for it. Make sure to state which
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