Calculus In Exercises 4346, let f and g be functionsin the vector space C[a, b] with

Chapter 5, Problem 44

(choose chapter or problem)

Calculus In Exercises 43 - 46, let f and g be functions in the vector space C [a, b] with inner product \(\langle f, g\rangle=\int_{a}^{b} f(x) g(x) dx\).

Show that \(f(x)=\sqrt{1-x^{2}}\) and \(g(x)=2 x \sqrt{1-x^{2}}\) are orthogonal in C[-1, 1].

Text Transcription:

langle f, g rangle = int_{a}^{b} f(x) g(x) dx

f(x) = sqrt{1 - x^2}

g(x) = 2x sqrt {1 - x^2}