Let {P, < > } be an inner product space with < p(x) | q(x) >...

 

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Let {P³, < > } be an inner product space with < p(x) | q(x) > = =√₁² p(x)q(x) dx A) Calculate ||x²|| B) Calculate ||x³ - 1|| C) Find the cosine of the angle between p(x) = x² and g(x) = x³ - 1. Is it acute or obtuse? D) Interpret the Cauchy-Schwarz inequality in terms of this inner product. Let {P³, < > } be an inner product space with < p(x) | q(x) > = =√₁² p(x)q(x) dx A) Calculate ||x²|| B) Calculate ||x³ - 1|| C) Find the cosine of the angle between p(x) = x² and g(x) = x³ - 1. Is it acute or obtuse? D) Interpret the Cauchy-Schwarz inequality in terms of this inner product.