Consider the function f : [0, 0) → [0, ∞0), f(x) = x + 1 Prove by induction that for any n E N f"(x) = 1 + nx where f" = f •f• ... • f (there are n copies of f on the right-hand side).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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PSH Q3

Consider the function f : [0, ∞) → [0, ∞), f(x) =
Prove by induction that for any n E N
x + 1
f"(x) =
1 + nx
where f" = f ofo ... • ƒ (there are n copies of f on the right-hand side).
Transcribed Image Text:Consider the function f : [0, ∞) → [0, ∞), f(x) = Prove by induction that for any n E N x + 1 f"(x) = 1 + nx where f" = f ofo ... • ƒ (there are n copies of f on the right-hand side).
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