sample1(mt1) for calculus 1

8/13/2019 Sample1(MT1) for calculus 1

1/8

1

THE AMERICAN UNIVERSITY IN CAIRO

School of Sciences & Engineering

Mathematics & Actuarial Science Department MACT-231

Time: 60 Minutes

Sample(1)

Question 1 20 pts

Question 2 20 pts

Question 3 20 pts

Question 4 20 pts

Bonus 6 pts

Total 80 pts

Total/4 20 pts

Name:______________________________________________

ID Number : ______________________________

Section: ------------------------------------------

First Mid-term


2/8

2

Answer the following questions:

Question 1: (20 pts)

Determine if each of the following sequences converges or diverges and find the limit whenever

possible:

a) nn2n5

2

2

,

b) 3nn3cos

,

c) )n3ln(n3

,

d) 1n,a4a,2a n1n1 .


3/8

3


Determine if each of the following series converges or diverges and find the sum whenever possible:

a) 2n nlnn 1

b)

1n

n

1n

4

39


4/8


5/8

5


a) Find the partial sum S4of the series 1n 7n1 and estimate the error in using it as an approximationto the sum of the series. How many terms need to be added to find the sum of the series accurate

to nine decimal places?


6/8

6

b) Find the interval of convergence and the radius of convergence for the power series: 1n

nn

3n

)3x(3 .


7/8

7


Find the Maclaurin series for xsin)x(f . Then use the obtained result to approximatedx

x

xsin1.0

0

accurate to four decimal places.


8/8

8

Bonus: (6 pts)

Find the power series expansion ofx

xtan 1. What is the radius of convergence?

(Hint: )xxx1x1

1 32

sample1(mt1) for calculus 1

Documents