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=0B.B. x-y+5=0x-y+5=0C.C. x+y+5=0x+y+5=0D.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= -2B.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. -2-2B.B. 33C.C. 22D.D. - 3- 3

41

3lim

xx

x25% 25%25%25%

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4.4.3

2 20

limxxx

x

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25% 25%25%25%

A.A. -æ (- infinity)-æ (- infinity)B.B. æ (+ infinity)æ (+ infinity)C.C. 00D.D. øø

5.5.

xx

x41

41

0lim

25% 25%25%25%

A.A. 00B.B. 1/161/16C.C. ØØD.D. -1/16-1/16

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6. Find the derivative of6. Find the derivative ofxxxy 132 2

25% 25%25%25%

2

1x

1.

2

2 12xx

2.

2

1x3.

x14.

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7. Find the derivative of7. Find the derivative of 22 9 xxy

25% 25%25%25%

xx

x 29

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 + 3B.B. 6x6x33 – 2x – 2x22 + 3 + 3C.C. 6x6x22 + 2x – 3 + 2x – 3D.D. 6x6x22 – 2x + 3 – 2x + 3

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9. Find the 29. Find the 2ndnd derivative of derivative of 21

x

y

A B C D

25% 25%25%25%

221

x

1.

222x

2.

21x

3.

322x

4.

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10. Using implicit differentiation solve10. Using implicit differentiation solveyxyx 33

25% 25%25%25%

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1331' 2

2

yxy

1.

1331' 2

2

yxy

2.

1'y3.

2

2

'yxy

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 existC.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 ]

xxxf 1)(

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25% 25%25%25%

A.A. x= -1x= -1B.B. x= -1/xx= -1/x22 C.C. x=1x=1D.D. x=5/2x=5/2

13.13.

1

31

2lim 2

xx

xx

x

25% 25%25%25%

A.A. Neg. infinityNeg. infinityB.B. Pos. infinityPos. infinityC.C. 55D.D. 00

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14.14.1

lim2 xx

x

25% 25%25%25%

A.A. Neg. infinityNeg. infinityB.B. Pos. infinityPos. infinityC.C. 55D.D. 00

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15.15.

13

12lim

xx

xx

x25% 25%25%25%A.A. Neg. infinityNeg. infinity

B.B. Pos. infinityPos. infinityC.C. 55D.D. 00

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16.16.3

5lim 2

xx

x25% 25%25%25%A.A. Neg. infinityNeg. infinity

B.B. Pos. infinityPos. infinityC.C. 55D.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%

61.

22.

33.

24.

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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. 1/61/6D.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 – 1C.C. -e-exx

D.D. -xe-xexx

20. Find the derivative of20. Find the derivative of 2

xx eey

25% 25%25%25%

211.

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 + cC.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

xx

3

2

3

25% 25%25%25%

cu ln311.

cx 33ln31

2.

cx 2ln31

3.

cx 2ln314.

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24. Differentiate in simplest form24. Differentiate in simplest form

1lnxxy

25% 25%25%25%

2)1(1

xxx

1.

1xx

2.

2)1( xx

3.

)1(1xx

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%

3321.

02.

316

3.

164.

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26. Evaluate26. Evaluate

A.A. 4040B.B. 420420C.C. 400400D.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=8B.B. A= -192; B=1A= -192; B=1C.C. A=192; B=1A=192; B=1D.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

23

4

243.

cxx

63 24

4.

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29. Evaluate29. Evaluate dx

xx

23

2

1

A B C D

25% 25%25%25%

cxx

43

3

1

1.

cx

3131

2.

433

1 xx

3.

3131x

4.

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30. Evaluate30. Evaluate

A.A. 33B.B. -3-3C.C. -1/3-1/3D.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. 2121B.B. 66C.C. 1515D.D. 2727

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