Question • Given ○ V=C([−1,1]) ○ ⟨v,w⟩=∫_(−1)^1▒v(x)w(x)dx • Find the linear polynomial closest to f(x)=e^x • Answer ○ Let S=span{1,x} ○ Projection of f onto S is ○ ⟨1,e^x ⟩/⟨1,1⟩ ⋅1+⟨x,e^x ⟩/⟨x,x⟩ ⋅x ○ Therefore the linear polynomial closest to f(x)=e^x is ○ g(x)=3/e x+(e−e^(−1))/2
