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lim<x→0> ∫<0, x^2> f(t)dt / [∫<0, x> f(t)dt]^2 (0/0)
= lim<x→0> xf(x^2) / [f(x) ∫<0, x> f(t)dt] (0/0)
= lim<x→0> [f(x^2) + 2x^2f'(x^2)] / [f'(x) ∫<0, x> f(t)dt + f^2(x)]
= lim<x→0> [0 + 2x^2] / [ ∫<0, x> f(t)dt + 0]
= lim<x→0> 2x^2 / ∫<0, x> f(t)dt (0/0)
= lim<x→0> 4x / f(x) (0/0)
= lim<x→0> 4 / f'(x) = 4
= lim<x→0> xf(x^2) / [f(x) ∫<0, x> f(t)dt] (0/0)
= lim<x→0> [f(x^2) + 2x^2f'(x^2)] / [f'(x) ∫<0, x> f(t)dt + f^2(x)]
= lim<x→0> [0 + 2x^2] / [ ∫<0, x> f(t)dt + 0]
= lim<x→0> 2x^2 / ∫<0, x> f(t)dt (0/0)
= lim<x→0> 4x / f(x) (0/0)
= lim<x→0> 4 / f'(x) = 4
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