Exercises: 1. Consider the Lagrange coefficient polynomial L2k(x) that are used for quadratic interpolation at the nodes x,X1, and x2. Define g(x)=L2,0(x)+L2,1(x)+L22(x)-1. a. Show that g is a...

Extracted text: Exercises: 1. Consider the Lagrange coefficient polynomial L2k(x) that are used for quadratic interpolation at the nodes x,X1, and x2. Define g(x)=L2,0(x)+L2,1(x)+L22(x)-1. a. Show that g is a polynomial of degree < 2.="" b.="" show="" that="" g(xg)="0" for="" k="0,1,2." 2.="" consider="" the="" function="" f(x)="sin(x)" on="" the="" interval="" [0,1].="" use="" theorem(3.3)="" to="" determine="" the="" step="" size="" h="" so="" that:="" a.="" linear="" lagrange="" interpolation="" has="" an="" accuracy="" of="" 10°.="" b.="" quadratic="" lagrange="" interpolation="" has="" an="" accuracy="" of="" 10°.="" c.="" cubic="" lagrange="" interpolation="" has="" an="" accuracy="" of="">