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Consider the vector space C[0,1] with inner product \int\limits_0^1 f(x)g(x) dx . (a) Determine whether the function f(x)=3x is a unit vector in this...

Consider the vector space C[0,1] with inner product01f(x)g(x) dx . 

(a) Determine whether the function f(x)=3x is a unit vector in this space. If it is, then show that it is. If it is not, then find a function that is.





(b)Find in exact form the cosine of the angle between f(x)= 5x^2 and g(x)=9x.  

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