1 - Swarthmore College
f(1000) = ( sqrt ( 1 – g(x)2 ) ≤ 1. and in particular, f(1000) < 1000. Second solution. The general solution of the system is. f(x) = A sin ( U(x) ) g(x) = A cos ( U(x) ) where A is any real number and U(x) is any function whose derivative is u(x). From the initial conditions, A must be 1. So, |f(x)| ≤ 1 for all x… ................
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