In calculus, you will learn that certain functions can be approximated by polynomial functions. We will explore one such function now.

(a) Using a graphing utility, create a table of values with

Y₁ = f(x) 1/1 – x and Y₂ = g₂(x) = 1 + x + x² + x³ for -1 < x < 1 with ΔTb1 = 0.1.

(b) Using a graph, utility, create a table of values with

Y₁ = f(x) = 1/1 – x and Y₃ = g₃(x) = 1 + x + x² + x³ + x⁴ for -1 < x < 1 with ΔTb1 = 0.1.

(c) Using a graphing utility, create a table of values with

Y₁ = f(x) = 1/1 - x and Y₄ = g₄(x) = 1 + x + x² + x³ + x⁴ + x⁵ for -1 < x < 1 with ΔTb1 = 0.1.

(d) What do you notice about the values of the function as more terms are added to the polynomial?Are there some values of x for which the approximations are better?