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1. Find the equation of the line through the point (-3,2) and perpendicular to the line x+y=7. x+y+1=0 x-y+5=0 x+y+5=0 X+y-1=0. 2. Find the equation of the line through the points (1,-2) and (3,-2). y= -2 y= ( 7 / 3 )x+y – ( 1 / 3 ) y= -7 / 3 7x+3y-1=0. 3. -2 3 2 - 3. 4. - PowerPoint PPT Presentation
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1. Find the equation of the line through the 1. Find the equation of the line through the point point (-3,2) and perpendicular to the line x+y=7(-3,2) and perpendicular to the line x+y=7
25% 25%25%25%A.A. x+y+1=0x+y+1=0
B.B. x-y+5=0x-y+5=0
C.C. x+y+5=0x+y+5=0
D.D. X+y-1=0X+y-1=0
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2. Find the equation of the line through the 2. Find the equation of the line through the points (1,-2) and (3,-2).points (1,-2) and (3,-2).
25% 25%25%25%A.A. y= -2y= -2
B.B. y= (y= (77//33)x+y – )x+y – ((11//33))
C.C. y= y= -7-7//33
D.D. 7x+3y-1=07x+3y-1=0
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3.3.
A.A. -2-2
B.B. 33
C.C. 22
D.D. - 3- 3
4
1
3
lim
x
x
x25% 25%25%25%
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4.4.3
2 2
0
lim
x
xx
x
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25% 25%25%25%
A.A. -æ (- infinity)-æ (- infinity)
B.B. æ (+ infinity)æ (+ infinity)
C.C. 00
D.D. øø
5.5.
xx
x41
41
0
lim
25% 25%25%25%
A.A. 00
B.B. 1/161/16
C.C. ØØ
D.D. -1/16-1/16
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6. Find the derivative of6. Find the derivative ofx
xxy
132 2
25% 25%25%25%
2
1
x
1.
2
2 12
x
x 2.
2
1
x
3.
x
14.
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7. Find the derivative of7. Find the derivative of22 9 xxy
25% 25%25%25%
xx
x2
9
22
1.
292 xx 2.
2
2
3
929
xxx
x
3.
22
92
xx
4.
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8. Find the derivative of8. Find the derivative of y=2xy=2x33 – x – x2 2 + 3x+ 3x
25% 25%25%25%A.A. 2x2x22 – x + 3 – x + 3
B.B. 6x6x33 – 2x – 2x22 + 3 + 3
C.C. 6x6x22 + 2x – 3 + 2x – 3
D.D. 6x6x22 – 2x + 3 – 2x + 3
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9. Find the 29. Find the 2ndnd derivative of derivative of 2
1
x
y
A B C D
25% 25%25%25%
221
x
1.
222
x
2.
2
1
x
3.
322
x
4.
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10. Using implicit differentiation solve10. Using implicit differentiation solve
yxyx 33
25% 25%25%25%
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13
31'
2
2
y
xy
1.
13
31'
2
2
y
xy
2.
1'y3.
2
2
'y
xy
4.
11. Use Rolle’s Th11. Use Rolle’s Thmm to help find the critical to help find the critical values of f(x)=xvalues of f(x)=x22 – 3x +2 – 3x +2
25% 25%25%25%
A.A. f(1)=f(2); crit# {-5/2}f(1)=f(2); crit# {-5/2}
B.B. No crit #’s existNo crit #’s exist
C.C. f(1)≠f(2); crit# {-5/2}f(1)≠f(2); crit# {-5/2}
D.D. f(1)=f(2); crit# {3/2}f(1)=f(2); crit# {3/2}
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12. Find the critical numbers for12. Find the critical numbers for
using the mean value thusing the mean value thmm on the interval [ ½ on the interval [ ½ , 2 ], 2 ]
x
xxf
1)(
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25% 25%25%25%
A.A. x= -1x= -1
B.B. x= -1/xx= -1/x22
C.C. x=1x=1
D.D. x=5/2x=5/2
13.13.
1
3
1
2lim 2
x
x
x
x
x
25% 25%25%25%
A.A. Neg. infinityNeg. infinity
B.B. Pos. infinityPos. infinity
C.C. 55
D.D. 00
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14.14.
1
lim2 x
x
x
25% 25%25%25%
A.A. Neg. infinityNeg. infinity
B.B. Pos. infinityPos. infinity
C.C. 55
D.D. 00
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15.15.
1
3
1
2lim
x
x
x
x
x25% 25%25%25%A.A. Neg. infinityNeg. infinity
B.B. Pos. infinityPos. infinity
C.C. 55
D.D. 00
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16.16.
3
5lim 2
x
x
x25% 25%25%25%A.A. Neg. infinityNeg. infinity
B.B. Pos. infinityPos. infinity
C.C. 55
D.D. 00
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17. Use the shell method to find the volume of the 17. Use the shell method to find the volume of the solid generated by revolving the given region about solid generated by revolving the given region about the y-axis. Graph is shown below. y=1-x, y=0; y-int the y-axis. Graph is shown below. y=1-x, y=0; y-int (0,1), x-int (1,0)(0,1), x-int (1,0)
25% 25%25%25%
6
1.
22.
3
3.
2
4.
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18. Find the area of the given region. 18. Find the area of the given region. f(x)=xf(x)=x22; g(x)=x; g(x)=x33 use your calculator to find use your calculator to find the intersections for this graph.the intersections for this graph.
25% 25%25%25%A.A. 1/3 1/3
B.B. 1/2 1/2
C.C. 1/61/6
D.D. 1/121/12
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19. Find the derivative of y=xe19. Find the derivative of y=xexx - e - exx
25% 25%25%25%
A.A. xexexx
B.B. xexexx – 1 – 1
C.C. -e-exx
D.D. -xe-xexx
20. Find the derivative of20. Find the derivative of 2
xx eey
25% 25%25%25%
2
11.
2
xe2.
2
xx ee 3.
04.
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21.21. dxeee xxx
25% 25%25%25%A.A. ½ e½ euu – x – x
B.B. ½ e½ e2x2x – x + c – x + c
C.C. 2e2x – x 2e2x – x
D.D. 2xe2xe2x 2x – 1 + c– 1 + c
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22.22. dxe x 2
1
1
25% 25%25%25%
ce11.
ce
12.
11e
3.
11
e
4.
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23.23. dx
x
x3
2
3
25% 25%25%25%
cu ln3
11.
cx 33ln3
12.
cx 2ln3
13.
cx 2ln3
14.
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24. Differentiate in simplest form24. Differentiate in simplest form
1lnx
xy
25% 25%25%25%
2)1(
1
xx
x1.
1xx
2.
2)1( xx
3.
)1(
1
xx
4.
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25. Find the volume of the solid formed by 25. Find the volume of the solid formed by revolving the given region about the x-axis, revolving the given region about the x-axis, using the Disc Method. Use your calculator using the Disc Method. Use your calculator
to find the points of intersection.to find the points of intersection. 24 xy
25% 25%25%25%
3
321.
02.
3
163.
164.
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26. Evaluate26. Evaluate
A.A. 4040
B.B. 420420
C.C. 400400
D.D. 42004200
25% 25%25%25%
20
1
2i
i
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27. Find 2 positive numbers that satisfy the 27. Find 2 positive numbers that satisfy the given requirement. The product is 192 and given requirement. The product is 192 and the sum of the first plus 3 times the second the sum of the first plus 3 times the second is the min.is the min.
25% 25%25%25%
A.A. A=24; B=8A=24; B=8
B.B. A= -192; B=1A= -192; B=1
C.C. A=192; B=1A=192; B=1
D.D. Not enough Not enough informationinformation
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28. Evaluate28. Evaluate dxxx )3( 2
25% 25%25%25%
cxx 331.
cx 33 22.
cxx
2
3
4
243.
cxx
6
3 244.
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29. Evaluate29. Evaluate dx
x
x23
2
1
A B C D
25% 25%25%25%
cx
x
43
3
1
1.
cx
313
12.
433
1 x
x
3.
313
1
x
4.
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30. Evaluate30. Evaluate
A.A. 33
B.B. -3-3
C.C. -1/3-1/3
D.D. 1/31/3
25% 25%25%25%
dxxx 1
0
21
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31. Evaluate31. Evaluate dx7
23
25% 25%25%25%
A.A. 2121
B.B. 66
C.C. 1515
D.D. 2727
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