Question

5) In Goy), with inner product < 1.8>]s«g(x)dx, let S(x)=x"$(x)=x', a) Computer />; b) Find the "angle" between the two functions.

Answer 1

a) If f(x) = x² and g(²) = x3 then <x², x3> x², x3 de 1 + 5 x dhe 1 + [24]. _ le (x², x3y = // ) If o be the angle between the two function f(x) and g(x) then Coso= <f, g) llfll 181 get in (a) / Now f(x) = x² g(x) = x3 and we <t,8) = 2x2, x3) 1 6 1811 Ft.<f, f) xixe² du it x4 de 7) IF!= V120) =

wp-v233) - Ta zo dx => 191- 16 Then coso <f, g) llfllllgll X - cosos V6 V735 COSO = 135 Thus the angle between two functions is Cos 054()