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A function y = f(x) satisfies (dy/dx) sin x - y cos x + (sin² x)/x² = 0 and y -> 0 as x -> infinity. Which statement is correct?
- lim x->0 f(x) = 1
- the integral of f(x) from 0 to pi/2 is less than pi/2
- the integral of f(x) from 0 to pi/2 is greater than unity
- f(x) is an odd function
Correct answer: lim x->0 f(x) = 1
Solution
Solving gives f(x) = sin x/x (after C = 0 from the boundary condition), so lim x->0 f(x) = 1.
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