Let f be continuous on [0, 1]. (a) Show that if f20 and f f(x) dx...

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Let f be continuous on [0, 1]. (a) Show that if f20 and f f(x) dx = 0, then f = 0 on [0, 1]. (b) If f f(x)r" dx = 0, for all n N, show that f = 0 on [0, 1]. [Hint: Use Weierstrass Approximation Theorem] Let f be continuous on [0, 1]. (a) Show that if f20 and f f(x) dx = 0, then f = 0 on [0, 1]. (b) If f f(x)r" dx = 0, for all n N, show that f = 0 on [0, 1]. [Hint: Use Weierstrass Approximation Theorem]

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