Calculus 2 Science

Final Exam Answers

Fall 1998

 

1) arcsin(2x)

2a)

 

2b)

 

2c)

 

2d)

 

2e) p

 

2f) ln(x+3) - (x-1)-1 + C

 

3a) Area = 71/3

3bi)

3bii)

 

4a) 0

4b) e3

4c)

 

5a) Integral is -1/ln(x) so it diverges

5b) Integral is 2/3 arctan(x/3) so it converges to p /3

 

6a) Converges by Ratio Test

6b) Diverges using nth term test

6c) Converges by Integral Test

6d) Diverges by Limit Comparison Test (use bn = n-1/2 )

 

7a) Not absolutely convergent, but does Converge by Alternating Series Test

7b) Absolutely Convergent and hence Convergent using Comparison with bn = 1/n2

8a) 1/10 , 1/8 , 3/22 , 1/7

8b)

8c) 1/6

 

9) Converges from -5 to 1. Converges at -5, but does not converge at 1.

 

10a) Converges for all real numbers by Ratio Test

10b) x2 - 1/6 x6 + 1/5! x10 - 1/7! x14 + 1/9! x18 + O(x20)