Question
Use Maclaurin series to approximate the integral \(\int_{0}^{1}\frac{e^{-x}-1}{x}dx\) to three decimal places.
(A) 1.387
(B) -0.796
(C) -2.558
(D) -0.288
Answer/Explanation
Ans:(B)
Question
Approximate \(\cos (9^{\circ})\) accurate to three decimal places.
(A) 0.891
(B) 0.951
(C) 0.982
(D) 0.987
Answer/Explanation
Ans:(D)
Question
Use the fourth-degree Taylor polynomial \(T_{4}(x)\) to approximate ln(2).
(A) \(\frac{2}{3}\)
(B) \(\frac{8}{11}\)
(C) \(\frac{7}{12}\)
(D) \(\frac{9}{13}\)
Answer/Explanation
Ans:(C)
One solution is to consider f(x)=ln(1-x), and notice that
(The constant of integration is 0, upon evaluation at x = 0.)
Therefore,\(T_{4}(x)=-x-\frac{1}{2}x^{2}-\frac{1}{3}x^{3}+\frac{1}{4}x^{4}\),and