Let f1,f0, and f1 denote the Lagrange polynomials associated with 1,0, and 1 respectively. (2.1) Find f1,f0, and f1 and express each one in standard polynomial form, that is, a+bx+cx2 where a,b, and c are real numbers. (2.2) Show that f1(x)=f1(x) and f1(x)=f1(x). (2.3) Show that f0 and f1

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Let f1,f0, and f1 denote the Lagrange polynomials associated with 1,0, and 1 respectively. (2.1) Find f1,f0, and f1 and express each one in standard polynomial form, that is, a+bx+cx2 where a,b, and c are real numbers. (2.2) Show that f1(x)=f1(x) and f1(x)=f1(x). (2.3) Show that f0 and f1+f1 are even. (2.4) Show fP2(R) is even if and only if fspan{f0,f1+f1}.

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