Problem 3. [20pts] Consider the vector space of continuous functions on [0,1] with the inner product...

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Problem 3. [20pts] Consider the vector space of continuous functions on [0,1] with the inner product explained in class, and consider the functions f(x) = e, g(x) = ex Using the inner product we can define a norm || || for functions. Determine the value of each of the following: 1. (4pts) (f,g) 2. (2pts) ||f| 3. (2pts) ||g|| 4. (4pts) |fg|| 5. (4pts) Find the 'angle' between f and g. 6. (4pts) Find the projection p of onto g. (f,g)= ||f|| ||9|| = ||f + g|| = P 0 = Problem 3. [20pts] Consider the vector space of continuous functions on [0,1] with the inner product explained in class, and consider the functions f(x) = e, g(x) = ex Using the inner product we can define a norm || || for functions. Determine the value of each of the following: 1. (4pts) (f,g) 2. (2pts) ||f| 3. (2pts) ||g|| 4. (4pts) |fg|| 5. (4pts) Find the 'angle' between f and g. 6. (4pts) Find the projection p of onto g. (f,g)= ||f|| ||9|| = ||f + g|| = P 0 =