Use the Maclaurin expansion for e- to express the function F(x) = f et dt as...

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Use the Maclaurin expansion for e- to express the function F(x) = f et dt as an alternating power series in x (Figure 1). (a) How many terms of the Maclaurin series are needed to approximate the integral for x = 1 to within an error of at most 0.001? (b) CAS Carry out the computation and check your answer using a computer algebra system. F(x) T₁(x) -X 2 -1² dt. FIGURE 1 The Maclaurin polynomial T₁5(x) for F(1) = -1² Jo Use the Maclaurin expansion for e- to express the function F(x) = f et dt as an alternating power series in x (Figure 1). (a) How many terms of the Maclaurin series are needed to approximate the integral for x = 1 to within an error of at most 0.001? (b) CAS Carry out the computation and check your answer using a computer algebra system. F(x) T₁(x) -X 2 -1² dt. FIGURE 1 The Maclaurin polynomial T₁5(x) for F(1) = -1² Jo

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