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Let f be differentiable with f'(x) = 7 - (3/4)*f(x)/x for x > 0 and f(1) != 4. Find the value of lim (x -> 0+) x*f(1/x).
- 4
- 7/4
- 4/7
- 28
Correct answer: 4
Solution
Solving gives f(x) = 4x + C*x^(-3/4); then x*f(1/x) = 4 + C*x^(7/4) -> 4 as x -> 0+.
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