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Show that

[tex] \lim_{n \rightarrow \infty} \int_{0}^{\pi} Ln(x) Sin(nx) dx [/tex]

i was told to use this identity

given that [itex] int f^2 \rho dx [/itex] is finite then

[tex] c_{n}^2 \int_{a}^{b} \phi_{n}^2 \rho dx = \frac{(\int_{a}^{b} f \phi_{n} \rho dx)^2}{\int_{a}^{b} \phi_{n}^2 \rho dx} \rightarrow 0 [/tex] and n approaches infinity

here Cn are the Fourier Coefficients

but how do i relate this to the problem i have

would rho = log x and phi^2 = sin nx?

Please help!

[tex] \lim_{n \rightarrow \infty} \int_{0}^{\pi} Ln(x) Sin(nx) dx [/tex]

i was told to use this identity

given that [itex] int f^2 \rho dx [/itex] is finite then

[tex] c_{n}^2 \int_{a}^{b} \phi_{n}^2 \rho dx = \frac{(\int_{a}^{b} f \phi_{n} \rho dx)^2}{\int_{a}^{b} \phi_{n}^2 \rho dx} \rightarrow 0 [/tex] and n approaches infinity

here Cn are the Fourier Coefficients

but how do i relate this to the problem i have

would rho = log x and phi^2 = sin nx?

Please help!

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