\phi_n g(x)=\int _{|x|\leq 1}f_n(x)(g(0)+h(x))dx+\int_{|x|> 1}f_n(x)g(x)dx=\int_{|x|\leq 1} \frac{n}{\sqrt{\pi}}e^{-n^2 x^2}g(0)dx+\int_{|x|\leq 1} \frac{n}{\sqrt{\pi}}e^{-n^2 x^2}h(x)dx+\int_{|x|> 1}\frac{n}{\sqrt{\pi}}e^{-n^2 x^2}g(x)dx