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6) Define the angle between two nonzero functions ƒ and g by with 0 ≤0πT. cos(0) (f,g) || f ||||g9|| a) If ƒ and g are orthogonal, show that b) If ƒ and g are proportional, show that c) If = 0 or 0 = = πT 2 = 0 or 0 =T. π, show that ƒ and g are proportional. (HINT: You can find a coefficient c so that ||f – cg||2 = 0. By the definition of - inner product, we must have f(x) = cg(x).) d) Compute the angle between f(x) = 1 and g(x) = x on 0 ≤ x ≤ 1.

6) Define the angle between two nonzero functions ƒ and g by with 0 ≤0πT. cos(0) (f,g) || f ||||g9|| a) If ƒ and g are orthogonal, show that b) If ƒ and g are proportional, show that c) If = 0 or 0 = = πT 2 = 0 or 0 =T. π, show that ƒ and g are proportional. (HINT: You can find a coefficient c so that ||f – cg||2 = 0. By the definition of - inner product, we must have f(x) = cg(x).) d) Compute the angle between f(x) = 1 and g(x) = x on 0 ≤ x ≤ 1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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6) Define the angle between two nonzero functions ƒ and g by with 0 ≤0πT. cos(0) (f,g) || f ||||g9|| a) If ƒ and g are orthogonal, show that b) If ƒ and g are proportional, show that c) If = 0 or 0 = = πT 2 = 0 or 0 =T. π, show that ƒ and g are proportional. (HINT: You can find a coefficient c so that ||f – cg||2 = 0. By the definition of - inner product, we must have f(x) = cg(x).) d) Compute the angle between f(x) = 1 and g(x) = x on 0 ≤ x ≤ 1.
Transcribed Image Text:6) Define the angle between two nonzero functions ƒ and g by with 0 ≤0πT. cos(0) (f,g) || f ||||g9|| a) If ƒ and g are orthogonal, show that b) If ƒ and g are proportional, show that c) If = 0 or 0 = = πT 2 = 0 or 0 =T. π, show that ƒ and g are proportional. (HINT: You can find a coefficient c so that ||f – cg||2 = 0. By the definition of - inner product, we must have f(x) = cg(x).) d) Compute the angle between f(x) = 1 and g(x) = x on 0 ≤ x ≤ 1.
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