2. Consider the Taylor polynomials of f(x) = √√x centered at x = 9. (a) Find T₁(x), T2(x), and T3(x). (b) Use Desmos to plot f(x) as well as the above Taylor polynomials on the same set of axes. (c) Use T₁(x), T2(x) and T3(x) to approximate √9.1. (d) Find the error in these approximations. The error is defined to be |√9.1 — TË(9.1)]. (Recall that |xy| is the "number line distance" between x and y.) (e) The Taylor Polynomial Error Bound guarantees that x - - |f(x) − Tn(x)| ≤ K · a|n+1 (n + 1)! " where K = maximum of f+1 (u)| on the closed interval between a and x, (provided f+1 exists and is continuous). What does the Error Bound guarantee about the size of √√9.1 - T3 (9.1)|? How does it compare to the actual error?

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