Rates/IntroRates/IntroRates/IntroRates/Intro

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LimitsLimitsLimitsLimits ContinuityContinuityContinuityContinuity Misc.Misc.Misc.Misc.

Chapter 2.1 to 2.5Chapter 2.1 to 2.5

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Review for the TestReview for the TestChapter 2.1 to 2.5Chapter 2.1 to 2.5

Final Round

InfinityInfinityInfinityInfinity

Rates

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F(-3) = -26F(-3) = -26

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10 Point Question10 Point Question

F(x) = -2xF(x) = -2x22 + x – 5. Find F(-3). + x – 5. Find F(-3).

Let G(x) = xLet G(x) = x22 + 2. Find the + 2. Find the average rate of change average rate of change between x=2 and x=5between x=2 and x=5

20 Point Question20 Point Question

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A.R.C. = 7A.R.C. = 7

The Federal Debt was growing by The Federal Debt was growing by 82,967 million dollars per year between 82,967 million dollars per year between

1999 and 2002.1999 and 2002.

30 Point Question30 Point Question

Find the average rate of change Find the average rate of change between 1999 and 2002. Give your between 1999 and 2002. Give your

answer in a complete sentence.answer in a complete sentence.

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The slope at C.The slope at C.

40 Point Question40 Point Question

What is bigger? The slope between the What is bigger? The slope between the points A & B, or the slope at C? points A & B, or the slope at C?

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An object’s height above the An object’s height above the ground (in feet) is given by h = -ground (in feet) is given by h = -16t16t22 + 6t+130. How fast is the + 6t+130. How fast is the

object traveling at t=3 seconds?object traveling at t=3 seconds?

50 Point Question50 Point Question

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The object is falling at a speed The object is falling at a speed of 90 feet per second.of 90 feet per second.

Limits

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/2/2

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Find the Find the limit:limit:

10 Point Question10 Point Question

25

xLim

20 Point Question20 Point Question

Find the limit:Find the limit:

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11

xx

xLim )sin(

0

30 Point Question30 Point Question

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Find the limit:

2

5158

5

2

xxx

xLim

Find the limit from the graphFind the limit from the graph

40 Point Question40 Point Question

44

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)(1

xfLimx

Sketch a graph with the following Sketch a graph with the following properties:properties:

50 Point Question50 Point Question

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Answers Answers may vary.may vary.

1)(3

xfLimx

2)(3

xfLimx

2)3( f

Infinity

Does Infinity + Infinity = Infinity?Does Infinity + Infinity = Infinity?

10 Point Question10 Point Question

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YesYes

Find the limit: Find the limit:

20 Point Question20 Point Question

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0xLimx

8

= 1= 1

Find the limit:Find the limit:

30 Point Question30 Point Question

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65

42

2

xx

xLimx

40 Point Question40 Point Question

Based on the graph, find Based on the graph, find

-infinity -infinity

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)(3

xfLimx

Find the Limit:Find the Limit:

InfinityInfinity

50 Point Question50 Point Question

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xxLimx

94 2

Continuity

f(a) must exist.f(a) must exist.The limit as x-> a of f(x) must exist.The limit as x-> a of f(x) must exist.

f(a) = limit as x->a of f(x)f(a) = limit as x->a of f(x)

10 Point Question10 Point Question

What are the requirements for a What are the requirements for a function to be continuous at the point function to be continuous at the point (a, f(a))?(a, f(a))?

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Daily Double: The team picking this Daily Double: The team picking this question gets 40 points!question gets 40 points!

20 Point Question20 Point Question

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No. Limit as x -> 5 is 3/8 (not No. Limit as x -> 5 is 3/8 (not 0.5)0.5)

Is this function continuous at x = 5?Is this function continuous at x = 5?30 Point Question30 Point Question

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5

5

,5.0

,25

153)( 2

x

xx

xxf

40 Point Question40 Point Question

What value must f(D) be to make What value must f(D) be to make the graph continuous?the graph continuous?

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33

50 Point Question50 Point Question

What value for c makes the function What value for c makes the function continuous at x = 3?continuous at x = 3?

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c = 5c = 5

3

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,

,1)( 2

x

x

cx

xxf

Miscelaneous

30 30

How many days are there in April?How many days are there in April?

10 Point Question10 Point Question

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Where is the Assessment and Testing Where is the Assessment and Testing Center?Center?

20 Point Question20 Point Question

RLC 173RLC 173

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30 Point Question30 Point Question

Who is the Vice President of the Who is the Vice President of the United States?United States?

Richard CheneyRichard Cheney

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40 Point Question40 Point Question

Where is your instructor’s Where is your instructor’s office?office?

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SMT 327SMT 327

What time does the What time does the Testing Center kick you Testing Center kick you

out on Friday?out on Friday?

50 Point Question50 Point Question

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4 PM4 PM

Just kidding. It Just kidding. It really is really is infinity.infinity.

If If

Final QuestionFinal Question

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28 )8(

1

xLimx

25 5

1

xLimx

ThenThen 5