Calculus I JeopardyCalculus I Jeopardy

Created Fall 2002Created Fall 2002

By Anne DudleyBy Anne Dudley

Glendale Community CollegeGlendale Community College

Modified Spring 2013 by Michael Modified Spring 2013 by Michael HoltfrerichHoltfrerich

Calculus Jeopardy Calculus Jeopardy FINAL

LIMITSDERIVA-TIVES

APPL. OF DERIVA-TIVES

INTE-GRATION

ALGE-BRA

MISC.

$100$100 $100$100 $100$100 $100$100 $100$100 $100$100

$200$200 $200$200 $200$200 $200$200 $200$200 $200$200

$300$300 $300$300 $300$300 $300$300 $300$300 $300$300

$400$400 $400$400 $400$400 $400$400 $400$400 $400$400

Limits $100Limits $100

What is

ANSWER

limx 0

sin xx

Limits $200Limits $200

What is

ANSWER

2

lnlimx

x

x

Limits $300Limits $300

What is

ANSWER

limx

3x3 4x2 7

5x2 6x3

Limits $400Limits $400

What is

ANSWER

limx 0

(1 x)1x

Derivatives $100Derivatives $100

What is the derivative of

Simplify your answer.

ANSWER

y cot(3x)

Derivatives $200Derivatives $200

What

ANSWER

What is the derivative of

Simplify your answer.

y 9x2 4

Derivatives $300Derivatives $300

What

ANSWER

What is the derivative of

Simplify your answer.

y x x ln x

Derivatives $400Derivatives $400

What

ANSWER

What is the derivative of

Simplify your answer.

y2 2xy 5

Applications $100Applications $100

For a function to have a minimum or a maximum, what has to happen to the derivative?

ANSWER

Applications $200Applications $200

What is a place on a curve called where concavity switches?

ANSWER

Applications $300Applications $300

What is the maximum area that can be enclosed with 100 feet of fencing, given the region below?

ANSWER

Applications $400Applications $400

List three words that you might find in an application problem that would signal you to take the derivative.

ANSWER

Integration $100Integration $100

What integral will measure the area shown below?

ANSWER

2 5

y = f(x)

Integration $200Integration $200

Evaluate

ANSWER

sin(3 )x dx

Integration $300Integration $300

Find and simplify:

ANSWER

ddx

tdt5

4 x

Integration $400Integration $400

Evaluate.

ANSWER

ln xdx

x

Algebra $100Algebra $100

Simplify completely:

ANSWER

36x2 18

Algebra $200Algebra $200

Simplify completely:

ANSWER

2x 3

2

32

Algebra $300Algebra $300

Simplify completely:

ANSWER

5 4 22 8

3

x x x

x

Algebra $400Algebra $400

Factor completely:

ANSWER

x3(2x 3) 1

2 (2x 3)1

2 (3x2 )

MISC $100MISC $100

Complete the square?

ANSWER

22 12 7x x

MISC $200MISC $200

Evaluate:

ANSWER

1cos(sin (1/ 2))

MISC $300MISC $300

Which is a better way to approximate an area, Trapezoid or Simpson’s Rule?

ANSWER

MISC $400MISC $400

How many different families of integrals have we learned this semester?

ANSWER

Limits $100Limits $100AnswerAnswer

Back to Jeopardy

limx 0

sin xx

1

Limits $200Limits $200AnswerAnswer

Back to Jeopardy

2

lnlim 0x

x

x

Limits $300Limits $300AnswerAnswer

Back to Jeopardy

limx

3x3 4x2 7

5x2 6x3 12

Limits $400Limits $400AnswerAnswer

Back to Jeopardy

limx 0

(1 x)1x e

Derivatives $100Derivatives $100AnswerAnswer

The derivative is

Back to Jeopardy

y 3csc2 (3x)

Derivatives $200Derivatives $200AnswerAnswer

The derivative is

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9x

9x2 4

Derivatives $300Derivatives $300AnswerAnswer

The derivative is

Back to Jeopardy

ln(x)

Back to Jeopardy

Derivatives $400Derivatives $400AnswerAnswer

The derivative is

yy

y x

Applications $100Applications $100AnswerAnswer

The derivative must equal ZERO or possibly undefined.

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Applications $200Applications $200AnswerAnswer

A place on the curve where concavity switched is called an INFLECTION POINT.

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Applications $300Applications $300AnswerAnswer

Area is 1250/3 square feet.

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Applications $400Applications $400AnswerAnswer

Some possibilities are:

Minimize, Maximize, Optimize,

Velocity, Acceleration,

Rate of Change, Slope of Tangent line

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Integration $100Integration $100AnswerAnswer

Back to Jeopardy

f(x)dx2

5

Integration $200Integration $200AnswerAnswer

Back to Jeopardy

13 cos(3x)C

Integration $300Integration $300AnswerAnswer

Back to Jeopardy

8 x

Integration $400Integration $400AnswerAnswer

Back to Jeopardy

2ln 1ln

2

xdx x C

x

Algebra $100Algebra $100AnswerAnswer

Back to Jeopardy

36x2 18 3 4x2 2

Algebra $200Algebra $200AnswerAnswer

Back to Jeopardy

43x x

OR 4

3x3

2

Algebra $300Algebra $300AnswerAnswer

Back to Jeopardy

4 3 2 1712 2 6 19 573

x x x xx

Algebra $400Algebra $400AnswerAnswer

Back to Jeopardy

2(7 9)

2 3

x x

x

MISC $100MISC $100AnswerAnswer

Back to Jeopardy

22( 3) 25x

MISC $200MISC $200AnswerAnswer

Back to Jeopardy

1 3cos(sin (1/ 2))

2

MISC $300MISC $300AnswerAnswer

Simpson’s (a curve is better than straight lines)

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MISC $400MISC $400AnswerAnswer

Five (power, exp, trig, ln, inverses)

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Final Jeopardy QuestionFinal Jeopardy Question

2

2 5

2 2

xdx

x x

Evaluate:

Answer

Final Jeopardy AnswerFinal Jeopardy Answer

2 1ln 2 2 7 ( 1)x x Tan x C

The End

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