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Unformatted text preview: Form B
Math 1206 Common Part 'of Final Exam May 10, 2005 INSTRUCTIONS: Please enter your NAME, ID NUMBER, FORM designation, and CRN
. on your op scan sheet. ‘The'CRNshould be written in the upper righthand box'labeled
"Course." Do not include the course number. in the box labeled "Form," write the
appropriate test form letter shown above. Darken the appropriate circles below your lD
number and Form designation. U.se.a #erpencil. Markyourna‘nswers to thetestaquestions in rowed15 of the :op—scan sheet. Youchave 4
hour to, complete this part of the final exam. Your scoreon this part of the final exam will be.
the number of correct answers. Turn in the op scan sheet with your answers and the
question sheets, including this coverpage, at the end of this part of the final exam. Any .
additional parts of the examwillbegin after all students have completed this commonpart. Exam Policies: You may not use a. book, notes, formula sheet, or'a calculator or
computer. Giving or_receiving unauthorized aid is an Honor Code Violation. . Signature
Name (printed) I l f
Student ID _# i 2
1'. The integral j ~33:— has value
‘ —1
(1) 1/2 (2) 3/2
(3) 7/4 ' , (4) No Value. Integral Diverges 2. Evaluate dX
‘ (X +1)(x + l) l (1) 1n(x2+1)+tan'1x—2mlx+1+c (2) tan'lx—Zlnlx+1I+C ' (3) 51n(x2+1)+31nx+1+c (4) 1n(X2+l)+1nlx+ll+C C
3
3. Calculate! de
x
1 21114X+31n2XX c 4 2 r c
(1) (2) [(2111 4+3ln x—x)1m]l (3) 4 (4) None of the above 4. The region bounded by the graph of y = e", the yaxis, and the line y = 2 is revolved about the
line x =  1. What is the volume of the solid? 2 1x12
(1) a! (lny)2dy (2) 27c]. (x+1)(2—e")dx
I 0
ln2 2
(3) 27:! x(ex—2)dx (4) 7c] (1+lny)2dy
0 1
dx
5. Inte ate ————
gr I x2+4x+13
(1) h1(x2+4x+l3)+C (2) 1 1n(X2+4x+13)+C
2x+4
(3) ltm—1[X+2)+c (4) tan—1(X—ﬂ)+c
3 3 \ 3
6. Evaluate 11m (1+2tanx)3/x
x—>0+
(1) e6 i (2) 6 I (3) 1 (4) Does not exist ‘ 7 7. Which of the following is the Simpson’s Rule approximation to J 1nx dx with 6 subintervals?
1 (1) lnl+ln2+ln3+ln7
(2) g[Zlnl+41n2+2h13+~+4ln6+2h17] (3) %[hil+21n2+21n3++21n6+1n,7] (4) . %[m1+41n2+21n3+~+41n6+h17 ] (7 O 8., Integrate J.le coskidx 3 (1) xzsinx‘t'erosx—Zsinx+ c (2) X?sinx+ c (3) XZSinXZXCOSX+23111X+ C (4) Xzsinx+xcosx+sinx+ C : Ssiﬂ[1 —9 "sequel to What integral?
4 n n  9. The limit hm ‘ k: 10 (I)! «(Ssinx dx _
1 I (3)! 1[Ssinx dX
1 . V 9 r r (2) I a/S sinx dx' _ . o _
(4) None of the above 10. Let R‘be the region bOunded bjthe graphs of "y x + 2 and y = X2. The vmomentvof the. region
about the yaXis and the y‘coordinate ofithe‘centroid‘are " ' ' “ :r  ~  ~ 2
M
(1) My=J X(X+1—X2)dX; V: y 2 . I g
' ' M
2 M = XX+1—x2 dX; —= X Area () (y I ( ) y «Area 1 —1 2 ' 2 '
1 ' 2 4. I My . 1 2 4 .5. M
3 M =— X+1 —x'* dx; = , 4 M =— X+l —X dx; x
0 y ZLR ) )1 yArea 0 y 2 _1[< ) )1 y
11. Find y(2) if y” = 4+—22— With initial conditions y'(1) = 5 and y (1) = 7
X. (1) 12+21n2 (2) 16—21n2 2
(3) j (4X +21n(x2) +1) dx (4) y is not deﬁned at X = 2
1 12. The integral dX .2 has thevalue
0 (X+2)
(1) —: 1/4 (2) 1/2
(3) 1/4 (4) No Value. Integral Diverges. 13. The region bounded by the graphs of y = x + 3 and y = X2 + l is revolved about the Xaxis.
What is the volume of the solid? 5 5
(1) 27c! yy/y—ldx (2) 2n! y(,/y—1—y+3)dx
l l 2 2
(3) R] [(x2+1)2—(x+3)2]dx (4) n! [(x+3)2—(x2+1)2]dx 1 —l 7
14. Evaluate 5t2 +1 dt
dx x2
(1) \/5x4+1 (2) —\/5x4+1
(3) —2x\/5x4+1 ‘ (4) 2xx/5x4+1 15. A ﬂat metal plate weighing 100 lbs is being pulled up the side of a 50 foot building by a rope
weighing 1/2 pound per linear foot. As it is pulled up the excess rope is dropped on the top of the
building. How much work (in foot pounds) is done in raising the plate from ground level to a point 20 feet above the ground? (1) 12520 (2) 10020 20 20
(3) j [MS—gjdx (4)! [100+3zijdx
0 _ _  0 ...
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This note was uploaded on 03/31/2008 for the course MATH 1206 taught by Professor Llhanks during the Spring '08 term at Virginia Tech.
 Spring '08
 LLHanks
 Calculus

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