Question: EXAMPLE 7 Using the Inner Product on C[0, 1] (Calculus) Use the inner product defined in Example 5 and the functions f(x) = x and

EXAMPLE 7 Using the Inner Product on C[0, 1] (Calculus) Use the inner product defined in Example 5 and the functions f(x) = x and g(x) = x2 in C[0, 1] to find each quantity. a. Ifll b. d(f, g) SOLUTION a. f(x) = x, so you have If\\R = - [(wax - [>ex - [sl! -3. So, IIfll = 3 b. To find d(f, g), write [d(f, 8) 12 = (f - 8, f - 8) = [ [f(x) - 8(x)Pdx = [x - x ] dx + 5 30 So, d( f, g) = 30

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