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Unformatted text preview: Modern Analysis 2
1. Let the diﬀerentiable function f : (−a, a) → R satisfy f (0) = 0 and
f = 1 + f 2 . By considering the function g := 2/f (or otherwise) show that
a is at most π/2.
Note: The cosine as the solution to a second-order IVP may be assumed, as
may its least positive zero. 1 ...
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- Spring '11