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)