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$V$ denotes real vector space $V$ consisting of all polynomials with real coefficients/any degree so $V$ is infinite dimensional. A symmetric bilinear form is defined on V by

$$(f,g) = \int_0^\infty f(x)g(x)e^{-x} dx$$

i) State briefly why this is positive definite on $V$ (may quote any general property of real integrals).

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