(a) sin 27 – sin 8

(b) 27 sin 27 – 8 sin 8

(c) cos 27 – cos 8

(d) 27 cos 27 – 8 cos 8

(a) 4.5e^{3}

(b) 2e^{3} + 1

(c) 4e^{3} – 1

(d) 3e^{3} – 3

(a) ln | x^{2 }– 1 | + C

(b) ln | x – 1 | – ln | x + 1 | + C

(c) (ln | x + 1 | – ln | x – 1 |) + C

(d) (ln | x – 1 | – ln | x + 1 |) + C

(a) [(x^{2} – 1) – (4x – 4)]dx

(b) [ (4x – 4) – ( x^{2} – 1) ]dx

(c) [(x^{2} – 1) – (4x – 4)]dx

(d) [ (4x – 4) – ( x^{2} – 1) ]dx

(a) e^{x} dx

(b) (e^{x})^{2} dx

(c) πe^{x} dx

(d) π(e^{x})^{2} dx

(a) L_{100} < I < T_{100} < R_{100}

(b) L_{100}< T_{100} < I < R_{100}

(c) R_{100}< I < T_{100} < L_{100}

(d) R_{100} < T_{100} < I < L_{100}

7. Consider the improper integral . Which of the following is true? (1 point)

(a) the integral converges to 0

(b) the integral converges to 0.5

(c) the integral converges to 1

(d) the integral diverges

8. What is the sum of the infinite series . . . ? (1 point)

(a) 0

(b) 1.5

(c) 2

(d) The series diverges

9) Consider the infinite series Which of the following is true? (1 Point)

(a) S_{1} converges and S_{2} converges

(b) S_{1} converges and S_{2} diverges

(c) S_{1} diverges and S_{2} converges

(d) S_{1} diverges and S_{2} diverges

10. Consider the infinite series Which of the following is true? (1 Point)

(a) S_{3} converges and S_{4} converges

(b) S_{3} converges and S_{4} diverges

(c) S_{3} diverges and S_{4} converges

(d) S_{3} diverges and S_{4} diverges

11. Which of the following is the Taylor series about x = 0 for sin x? (1 Point)

(a)

(b)

(c)

(d)

12. Which of the following is the second degree Taylor polynomial about x = 4 for (1 Point)

(a) – 1 < x < 1

(b) – 1 < x ≤ 1

(c) – 1 ≤ x < 1

(d) – 1 ≤ x ≤ 1

(a) y = 2e^{6t}

(b) y = e^{6t } + 1

(c) y = 3y^{2 } + 2

(d) y = 3t^{2 } + 2