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⎡⎛6.1 Introductory Calculus • 211⎞⎤⎧⎛⎨1 √⎞ ⎜1 ⎝ 2 1/2 √ 5 − 1/2√√5 − ⎜⎩arctan ⎝2 √ 2−2 + 2 √ 5 1 + 4 (1/2 √ ⎟5 − 1/2) 22 ⎟√ ⎠ , e−2 + 2 √ ⎠5,−2 + 2 5 ⎢⎥⎣⎦⎡⎛⎞⎤⎛1 √⎞ ⎜1 ⎝ 2 1/2 √ 5 − 1/2√ √ 5 − −2 + 2 5√1 ⎜−arctan ⎝2 √ 2+ 4 (1/2 √ ⎟5 − 1/2) 22 ⎟√ ⎠ + π, e−2 + 2 √ ⎠⎫5⎬−2 + 2 5 ⎭⎢⎥⎣⎦> evalf( % );{[0.6662394321, 1.855276958],[2.475353222, 1.855276958]}Since f is periodic, it has, of course, infinitely many inflection points.You can obtain these by shifting the two inflection points above horizontallyby integer multiples of 2π.A Taylor ApproximationThis section illustrates how you can use Maple to analyze the error termin a Taylor approximation. The following is Taylor’s formula.> taylor( f(x), x=a );f(a) + D(f)(a) (x − a) + 1 2 (D(2) )(f)(a) (x − a) 2 + 1 6 (D(3) )(f)(a)(x − a) 3 + 124 (D(4) )(f)(a) (x − a) 4 + 1120 (D(5) )(f)(a) (x − a) 5 +O((x − a) 6 )