5) Let S = {1, 02, 03, 04} be an orthonormal set of functions on −1 ≤ x ≤ 1 using the usual inner products for functions. Suppose that functions f and g are given by f(x) = a11(x) + α202(x) + α303(x) + α404(x), g(x) = b₁₁(x) + b22(x) + b303(x) +b404(x). a) Show that (f, g) = a1b1 + a2b2+ a3b3 + a4b4. b) What does the result from a) remind you of?
5) Let S = {1, 02, 03, 04} be an orthonormal set of functions on −1 ≤ x ≤ 1 using the usual inner products for functions. Suppose that functions f and g are given by f(x) = a11(x) + α202(x) + α303(x) + α404(x), g(x) = b₁₁(x) + b22(x) + b303(x) +b404(x). a) Show that (f, g) = a1b1 + a2b2+ a3b3 + a4b4. b) What does the result from a) remind you of?
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Transcribed Image Text:5) Let S = {1, 02, 03, 04} be an orthonormal set of functions on −1 ≤ x ≤ 1
using the usual inner products for functions. Suppose that functions f and
g are given by
f(x) = a11(x) + α202(x) + α303(x) + α404(x),
g(x) = b₁₁(x) + b22(x) + b303(x) +b404(x).
a) Show that (f, g) = a1b1 + a2b2+ a3b3 + a4b4.
b) What does the result from a) remind you of?
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