Question: (a) Write down the explicit formulae for the Cauchy-Schwarz and triangle inequalities based on the weighted inner product. (b) Verify that the inequalities hold when

(a) Write down the explicit formulae for the Cauchy-Schwarz and triangle inequalities based on the weighted inner product.

(b) Verify that the inequalities hold when fix) = 1, g(x) = ex by direct computation.
(c) What is the "angle" between these two functions in this inner product?

(f, g) f(x)g(x)e dx.

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