Suppose you approximate sin x at the points x = -0.2, -0.1, 0.0, 0.1, and 0.2 using the Taylor polynomials p₃ = x - x³/6 and p₅ = x - x³/6 + x⁵/120. Assume that the exact value of sin x is given by a calculator.

a. Complete the table showing the absolute errors in the approximations at each point. Show two significant digits.

b. In each error column, how do the errors vary with x? For what values of x are the errors the largest and smallest in magnitude?

X -0.2 -0.1 0.0 0.1 0.2 Error = sinx - P3(x)| Error = |sinx - P(x)|