If the series tan−1 is used to approximate with an error less than 0.001, then
the smallest number of terms needed is
(A) 100
(B) 200
(C) 300
(D) 400
(E) 500
Let f be the Taylor polynomial P 7 (x) of order 7 for tan−1 x about x = 0. Then it follows that, if
−0.5 < x < 0.5,
(A) f (x) = tan−1 x
(B) f (x) ≤ tan−1 x
(C) f (x) ≥ tan−1 x
(D) f (x) > tan−1 x if x < 0 but < tan−1 x if x > 0
(E) f (x) < tan−1 x if x < 0 but > tan−1 x if x > 0
Replace the first sentence in Question 19 by “Let f be the Taylor polynomial P 9 (x) of order 9
for tan−1 x about x = 0.” Which choice given in Question 19 is now the correct one?
Part B. Directions: Some of the following questions require the use of a graphing calculator.
Which of the following statements about series is false?
(A) where m is any positive integer.
(B) If converges, so does if c ≠ 0.
(C) If and converge, so does where c ≠ 0.
(D) If 1000 terms are added to a convergent series, the new series also converges.
(E) Rearranging the terms of a positive convergent series will not affect its convergence or its
sum.
