The function f(x) = 1/(x+1) is given. Using the points x 0 =0, x 1 =0.3, x 2 =0.4, x 3 =0.5; a) Write the P 3 (x) Lagrangian interpolation polynomial ; b) Calculate the value of f(0.2) and P 3 (0.2);...

The function f(x) = 1/(x+1) is given. Using the points x₀
=0, x₁
=0.3, x₂
=0.4, x₃
=0.5;

a) Write the P₃(x) Lagrangian interpolation polynomial ;

b) Calculate the value of f(0.2) and P₃(0.2);

c)Determine the upper limit of error at x= 0.2 using the remainder term expression;