SHORT ANSWERS TO OLD FINAL EXAM

1. 4 arctan3 3

yy c − +

2. (500 )dp k pdt

= −

3. 21arcsin(3 ) 1 93

x x x c+ − +

4. 2 316 tan sec dθ θ θ∫ 5. 23ln ln 1t t c− + +

6. a) 1

( )n

ii

H B x xB=

− ∆∑ b)

0( )

B Hkx B x dxB

⋅ −∫

7.

12 2

362.4 (2) ( 5)x dxπ +∫ one possibility

8. a) converges b) converges c) diverges

9. a) 4 3

1( )( 1)

f xx

=−

has a vertical asymptote inside the interval at 1x = . b) diverges

10. a) converges b) impossible to tell c) diverges

11. a) 4 6 8

2

2 3 4x x xx− − − − + b)

3 5 7

3 10 21x x x

− − −

12. ( ) 2

0 2kxe dx

kππ

∞ − =∫

13. ( )2 8

0

166

y y dy −

− −

∫

14. 7, 7B B= = −

b) ( ) 10 2

05 ( )f x dxπ −∫ 15. a)

16. Converges (use the Ratio Test).

17. a) The sequence converges to 35

. b) The series is geometric with 2 15

r = < .

c) The series converges to xe .

18. 2 1yz e +=

19. a) 22

5( ) 3 2( 1) ( 1)2

P x x x= − − + − b) (1.1) 2.825f ≈

20. 32

−