calclus quiz, show all work

Online MAC 2312 Calculus 2

Quiz 2

Welcome to your second Quiz! For all questions, please show your work. This allows me to provide

helpful feedback and appropriately assign partial credit. Correct answers without supporting work will

not receive credit.

1) For ∫ 1

ln𝑥 𝑑𝑥

4

2 Show all work and round your answer to 6 decimal places. You do not need to provide

a drawing.

a. Use the Trapezoidal Rule with 𝑛 = 4 to approximate the integral

b. Use the Midpoint Rule with 𝑛 = 4 to approximate the integral

c. Use Simpson’s Rule with 𝑛 = 4 to approximate the integral

d. What is the largest error that results from estimating the integral with Trapezoid Rule with

𝑛 = 4 (your calculation from part a)?

2) Evaluate ∫ 1

(2𝑥+1)3 𝑑𝑥

∞

1 or show that it is divergent

3) Evaluate ∫ ln𝑥

𝑥

∞

1 𝑑𝑥 or show that it is divergent.

4) Find a general term 𝑎𝑛 of the sequence

a. { 1

3 , 1

9 , 2

27 , 6

81 , 24

243 , 120

729 ⋯}

b. {3,8,13,18,23,…}

5) Determine whether the geometric series is convergent or divergent. Include your reasoning for your

conclusion. If it is convergent, find its sum.

a. 2 + 0.5 + 0.125 + 0.03125 + ⋯

b. ∑ 3𝑛+1

(−2)𝑛 ∞ 𝑛=0