review for calculus midyear exam. please select a team. 1.rico starr 2.the bushbabies 3.smoldering...

Review for Calculus Midyear Exam

Please select a Team.

Team 1

Team 2

Team 3

Team 4

Team 5

0% 0% 0%0%0%

1. Rico StaRR

2. The Bushbabies

3. Smoldering Marshmallows

1. From David:Evaluate the limit.

2

4lim

2

0

x

xx

0 -2

Does n

ot exis

t

0% 0%0%

1. 0

2. -2

3. Does not exist

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2. From Joe. Evaluate.

)(lim7xf

x

2 3 -7 D

NE

0% 0%0%0%

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1. 2

2. 3

3. -7

4. DNE

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3. From Will.Which of the following is not true?

)(lim

1)(lim

)(lim

)(lim

)(lim

0

2

2

0

xf

xf

xf

xf

xf

x

x

x

x

x

A) B) C) D) E)

0% 0% 0%0%0%

1. A)

2. B)

3. C)

4. D)

5. E)

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4. From Erica.

Why is the function discontinuous at x = -3?

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1. The function doesn’t exist at the same place where it’s defined

2. The function is undefined

3. The limit doesn’t exist

4. The limit doesn’t exist at the same place where the

function is defined

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5. From Meritt. How would you describe the function

between (-3,3) given the following table?

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1. Increasing, concave up

2. Increasing, concave down

3. Concave down, decreasing

4. Decreasing, concave up

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6. From Molly. Is the sketch on the right the derivative of the sketch on the left?

0%0%

1. Yes

2. No

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7. From Nick. Which point(s) on the given function have a tangent line parallel to the line given?

52

2

1

3

1)( 23

yx

xxxf

X=1,2

X=-1,-2

X=1, -2 X=2

0% 0%0%0%

1. X=1,2

2. X=-1,-2

3. X=1, -2

4. X=2

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8. From Sarah. What is the slope of the function at x=0?

32 8)4cos()( xxxf

0% 0%0%0%

1. 0

2. 1

3. -1

4. 0.5

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9. From Emily. Looking at the graph of f’(x),

on what intervals is f(x) decreasing?

),7)(5,1(

),10)(5,(

0% 0%0%0%

1. 1. (-5, 10)

2. 2.

3. 3.

4. 4. (-1, 10)

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10. From Jessica.True or False.

The given function is decreasing on the interval (-1,0).

23

2

1

3

1)( xxxf

0%0%

1. True

2. False

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11. From Patrick.

Nathaniel is stuck on a train that is moving back and forth. To help save him, you must figure out when the car is stopped before it starts moving

in the other direction because this is the best time to jump aboard. Nathaniel is counting on you. You are his only hope. Between 0 and 10

second, where does the train stop?

2483

1)( 23 tttts

4 2 -4 -8

0% 0%0%0%

1. 4

2. 2

3. -4

4. -8

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12. From Mo. What is the acceleration equation of this

function? ttttts 625)( 234

4660)(

6415)(

4660)(

64320)(

2

34

23

23

ttta

tttta

ttta

tttta

0% 0%0%0%

1. 1.

2. 2.

3. 3.

4. 4.

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13. From Sky. The position of a small pony is modeled by the equation below. At 2 seconds, its instantaneous velocity

is 13 mph.True or False.

1052)( 2 xxxs

True

False

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1. True

2. False

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14. From Fed.Find the derivative of f(x).

1

2)(

x

xxf

1. 2. 3. 4.

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1. 1.

2. 2.

3. 3.

4. 4.

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1

2)('

)1(

2)('

1

24)('

)1(

24)('

2

2

xxf

xxf

x

xxf

x

xxf

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15. From Bryan. Find the firs derivative.

)63(cos)() 2' xxxfA

)3(sin)( 2xxxf

)sin(cos)(') xxxxfB

)cos1(sin)() 2' xxxfC

)sin2cos(3)(') xxxxxfD

0% 0%0%0%

1. 1.

2. 2.

3. 3.

4. 4.

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16. From Dan.Find the derivative.

2)cos()('

2)cos()('

2)sin()('

2)sin()('

22

22

22

22

xx

xx

xx

xx

eexf

eexf

eexf

eexf

)sin()( 2xexf

0% 0%0%0%

1. 1.

2. 2.

3. 3.

4. 4.

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17. Evaluate the limit.

x

xxx

5lim

2

0

0 D

NE 5x 5

0% 0%0%0%

1. 0

2. DNE

3. 5x

4. 5

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18. Evaluate.

)24)(2(

32lim

2

xx

xxx

Infinity -1 -2 2

0% 0%0%0%

1. Infinity

2. -1

3. -2

4. 2

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19. At which x-value(s) is the function discontinuous?

232

121

13

)(

xx

x

xx

xf

1 -2

Both 1 and -2

None of t

he above

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1. 1

2. -2

3. Both 1 and -2

4. None of the above

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20. Consider the following information regarding f(x).What is the best description of f(x) at x=2?

f’(x) > 0 and f’’(x) < 0 for -1 < x < 2f’(2) = 0,

f’(x) < 0 and f’’(x) < 0 for x > 2.

Maxim

um

Inflecti

on point

X-interce

pt

Minim

um

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1. Minimum

2. Inflection point

3. X-intercept

4. Maximum

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21. Evaluate.

)(lim9

xfx

0% 0%0%0%

1. -2

2. 2

3. -9

4. DNE

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22. In order, identify f(x), f’(x), f’’(x).

Blue, purp

le, gray

Purple, g

ray,

blue

Gray

, purp

le blue

0% 0%0%1. Blue, purple, gray

2. Purple, gray, blue

3. Gray, purple blue

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23. To find the slope of a tangent line of f(x) which is parallel to a given line, you must set _____

equal to the ____ of the given line.

f(x);

derivative

f(x);

slope

f’(x);

x-inte

rcept

f’(x);

slope

0% 0%0%0%

1. f(x);derivative

2. f(x);slope

3. f’(x);x-intercept

4. f’(x);slope

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24. Given the functionbelow, which intervals is it both concave up

and decreasing?

42)( 34 xxxf

)2

3,(

),(

),0)(1,2

3(),

2

3,(

),0)(1,(

0% 0%0%0%

1. 1.

2. 2.

3. 3.

4. 4.

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25. The position of a cheetah is demonstrated by the function

below. What is the average velocity over the first two seconds?

)1(3)( 2 xxs x

44pmh

33 mph

22mph

0% 0%0%

1. 44pmh

2. 33 mph

3. 22mph

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26. In a period of 10 seconds, Boris is doing a volleyball suicide. The

following function traces his movement. Which way is he going

at the 1st second?xxxxf 203

3

2)( 23

Left

Right

Stopped

0% 0%0%

1. Left

2. Right

3. Stopped

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27. Given the function below, write an equation of the tangent

line drawn at x=2.

3

9)(x

xf

)2(16

27

8

9

)8

9(

16

272

)2(16

27

8

9

xy

xy

xy

1. 2. 3.

0% 0%0%

1. 1.

2. 2.

3. 3.

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28. On what intervals is f(x) concave up?

),5.3)(2,(

)3,1)(2,(

)5.3,2(

)5.3,1)(2,(

1. 2. 3. 4.

0% 0%0%0%

1. 1.

2. 2.

3. 3.

4. 4.

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29. A particle is moving left and right on a number line following the position of the function below. On

the interval of 1 to 10 seconds, when is the particle slowing down?

86)( 2 xxxs

0% 0%0%

1. Between 1 and 2 seconds

2. Between 1 and 3 seconds

3. Between 3 and 10 seconds

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30. Find the derivative.

2

2

2

2

2

2

2

2

)3(

)4)(3(ln)2)(3()('

)3(

)4)(3)(3(ln)2)(3()('

)3(

)4)(3)(3(ln)2)(3()('

)3(

)4)(3(ln2)('

x

x

x

xx

x

xx

x

xxxf

xxxf

xxxf

xxxf

x

xxf

3

4)(

2

1. 2. 3. 4.

0% 0%0%0%

1. 1.

2. 2.

3. 3.

4. 4.

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31. At which x-values does the following function have a horizontal tangent line?

xexxf 2)(

0% 0%0%0%

1. X=1, -2

2. X=0, -2

3. X=1, 0

4. X=-2 only

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32. Derive.

xxxf 7)( 2

xx

xxf

xx

xxf

xx

xxf

7

7)('

72

72)('

72

2)('

2

2

2

1. 2. 3.

0% 0%0%

1. 1.

2. 2.

3. 3.

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And now, the real test…

33. In which room is your Midyear exam ?

H4

H1

ME5

ME2

0% 0%0%0%

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1. H4

2. H1

3. ME5

4. ME2

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34. Who is the assigned proctor to your exam?

Mrs.

Lahey

Mrs.

Lehmann

Mr. K

eaney

Mr. C

handler

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1. Mrs. Lahey

2. Mrs. Lehmann

3. Mr. Keaney

4. Mr. Chandler

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35. Are you allowed to use a calculator on your exam?

No

Yes

0%0%

1. No

2. Yes

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Last Question…

Derive.

yxyxyx 22 2

2

2

22

221

221

22

yyx

xyx

dx

dy

xyx

yyx

dx

dy

1. 2.

0%0%

1. 1.

2. 2.

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