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Define \(\displaystyle f_{n}(x)=\frac{n^{1.5}x}{1+n^{2}x^2}\) for x in [0,1]. Use Dominated convergence theorem to find the limit of the integral of f_n over [0,1].

I find that f_n converges to 0 so if I can find domination function I have shown integral is zero. Correct? I find f_n is dominated by function g where g(x)=x^-2 when x is not zero and g(0)=0. Is such a function integrable?

Thanks

I find that f_n converges to 0 so if I can find domination function I have shown integral is zero. Correct? I find f_n is dominated by function g where g(x)=x^-2 when x is not zero and g(0)=0. Is such a function integrable?

Thanks

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