© mark e. damon - all rights reserved jeopardy directions for the game: 1. you will need a pencil...

© Mark E. Damon - All Rights Reserved

JeopardyDirections for the game:

1. You will need a pencil and paper to keep score. 2. On the next screen, click ONCE on a question. 3. Read the Question and decide on your answer. 4. Click ONCE on the screen If you’re right, add your

points to your total. If you are wrong, subtract those points.

5. Click ONCE on the button to go back to try another question.

6. Ready? Click ONCE to go the the Jeopardy board! 7. Press the “Esc” button on the keyboard to end the game.

Have fun!

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Derivatives Limits Integrals

Applications Misc.

Other stuff

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

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

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

$500 $500 $500 $500 $500 $500

Final Jeopardy

Scores


$100$100

Calculate the derivative of

ex


ex


$100$100

exex

Home


$200$200


f(x) = x sin (x)


f(x) = x sin (x)


$200$200

f’(x) = x cos (x) + sin (x)f’(x) = x cos (x) + sin (x)

Home


$300$300


Y = X2(X- 2)5


Y = X2(X- 2)5


$300$300

Home

y’ = 5x2(x-2)4 + (x-2)5(2x)

y’ = x(x-2)4(7x-4)

y’ = 5x2(x-2)4 + (x-2)5(2x)

y’ = x(x-2)4(7x-4)


$400$400

Use Implicit Differentiation to calculate y’

X2 + XY + Y3 = 3

Use Implicit Differentiation to calculate y’

X2 + XY + Y3 = 3


$400$400

2x + xy’ + y + 3y2 y’ = 0

y’ = -2x – y

X + 3y2

2x + xy’ + y + 3y2 y’ = 0

y’ = -2x – y

X + 3y2

Home


$500$500

Find the derivative of the following function

F(x) = x3 – 3x2 + 4

x2

Find the derivative of the following function

F(x) = x3 – 3x2 + 4

x2


$500$500

y’ = x3-8

x3

y’ = x3-8

x3

Home


$100$100

Evaluate

Lim 6X - 3

Evaluate

Lim 6X - 3X → 4X → 4


$100$100

2121

Home


$200$200

Evaluate

Lim sin x

x

Evaluate

Lim sin x

xX → 0X → 0


$200$200

1 1

Home


$300$300

Evaluate

Lim l x – 4 l

x - 4

Evaluate

Lim l x – 4 l

x - 4X → 4X → 4


$300$300

No limitNo limit

Home


$400$400

Evaluate

Lim X2 – 9

X + 3

Evaluate

Lim X2 – 9

X + 3X → - 3X → - 3


$400$400

-6-6

Home


$500$500

Evaluate

Lim (X + ΔX)2 + 1 – (X2 + 1)

ΔX

Evaluate

Lim (X + ΔX)2 + 1 – (X2 + 1)

ΔXΔX → 0ΔX → 0


$500$500

(X+ΔX)^2 + 1 – X^1 -1 Δ X cancel 1’s

X^2 + 2XΔX + ΔX^2 – X^2 Δ X square and simplify

2X + Δ XΔ X = 0Answer = 2X.

(X+ΔX)^2 + 1 – X^1 -1 Δ X cancel 1’s

X^2 + 2XΔX + ΔX^2 – X^2 Δ X square and simplify

2X + Δ XΔ X = 0Answer = 2X.

Home

2X2X


$100$100

Evaluate

∫ 2x dx

Evaluate

∫ 2x dx


$100$100

x2 + cx2 + c

Home


$200$200

Evaluate

∫ x3 + 2x

x

Evaluate

∫ x3 + 2x

x


$200$200

1/3 x3 +2x + c

(cancel one x and then integrate)

1/3 x3 +2x + c

(cancel one x and then integrate)Home


$300$300

Evaluate

∫ (lnx)3 dx

x

Evaluate

∫ (lnx)3 dx

x


$300$300

Let U = Lnx, du = 1/x dx

= ¼ (ln x)4 + c

Let U = Lnx, du = 1/x dx

= ¼ (ln x)4 + c

Home


$400$400

Evaluate

∫ cos 2x dx

Evaluate

∫ cos 2x dx


$400$400

½ sin(2x) + c½ sin(2x) + c

Home


$500$500

Evaluate

∫xe-x2 dx

Evaluate

∫xe-x2 dx


$500$500

Let u = -x2, du = -2x

-½ ∫ eu du

-½ e-x2+c

Let u = -x2, du = -2x

-½ ∫ eu du

-½ e-x2+c

Home


$100$100

In an application problem relevant to motion, the first

derivative of an equation tells ____________.

In an application problem relevant to motion, the first

derivative of an equation tells ____________.


$100$100

VelocityVelocity

Home


$200$200

In an application problem relevant to motion, the second

derivative tells ______________.

In an application problem relevant to motion, the second

derivative tells ______________.


$200$200

AccelerationAcceleration

Home


$300$300

A hot-air balloon is rising straight up from a level field and is being tracked by a range finder located

500ft from the balloon. At the moment the range finder’s angle of elevation is π/4, the angle is increasing at the rate of 0.14

rad/min. How fast is the balloon rising at that moment?

A hot-air balloon is rising straight up from a level field and is being tracked by a range finder located

500ft from the balloon. At the moment the range finder’s angle of elevation is π/4, the angle is increasing at the rate of 0.14

rad/min. How fast is the balloon rising at that moment?


$300$300 Draw a picture

Θ = the angle the range finder makes with the ground

Y = the height of the balloon (in feet)

T = time, and θ and y are differentiable functions of t.

Y = 500 tan θ

Y’ = 500 (sec2θ)dθ/dt

Y’ = 500(2)(.14) = 140ft/min

Draw a picture

Θ = the angle the range finder makes with the ground

Y = the height of the balloon (in feet)

T = time, and θ and y are differentiable functions of t.

Y = 500 tan θ

Y’ = 500 (sec2θ)dθ/dt

Y’ = 500(2)(.14) = 140ft/minHome


$400$400

Air is being pumped into a spherical balloon to cause its

volume to increase at a rate of 100cm3/s. How fast is the radius of the balloon increasing when the

diameter is 50 cm?

Air is being pumped into a spherical balloon to cause its

volume to increase at a rate of 100cm3/s. How fast is the radius of the balloon increasing when the

diameter is 50 cm?


$400$400

1/(25π) cm/s1/(25π) cm/s

Home


$500$500

Car A is traveling west at 50 mi/h while car B is traveling north at 60 mi/h. Both cars are headed

towards intersection C. At what rate are the cars approaching

each other when car A is 0.3 mi from the intersection, and car B is 0.4 mi from the intersection?

Car A is traveling west at 50 mi/h while car B is traveling north at 60 mi/h. Both cars are headed

towards intersection C. At what rate are the cars approaching

each other when car A is 0.3 mi from the intersection, and car B is 0.4 mi from the intersection?


$500$500

- 78 mi/h- 78 mi/h

Home


$100$100

Find the derivative of

y = ln(x3 + 1)


y = ln(x3 + 1)


$100$100

y’ = 3x2

X3+ 1

y’ = 3x2

X3+ 1

Home


$200$200


y = 6(x2)


y = 6(x2)


$200$200

y’ = (ln 6)(6^x^2)(2x)y’ = (ln 6)(6^x^2)(2x)

Home


$300$300

Find the second derivative of

y = x3 + 3x2 – ½ x + 5

Find the second derivative of

y = x3 + 3x2 – ½ x + 5


$300$300

Home

y = x3 + 3x2 – ½ x + 5

y’ = 3x2 + 6x – ½

y” = 6x + 6

y = x3 + 3x2 – ½ x + 5

y’ = 3x2 + 6x – ½

y” = 6x + 6


$400$400

Find y’

y = ln [x(1+x)2]

Find y’

y = ln [x(1+x)2]


$400$400

y’ = lnx +2ln(1+x)

y’ = 1/x +2/(1+x)

y’ = lnx +2ln(1+x)

y’ = 1/x +2/(1+x)

Home


$500$500

A farmer has 2400 feet of fencing to create a rectangular pen for his

lamas next to their new barn. If the barn side off the pen does not

need a fence, what are the dimensions of the pen with the

largest area?

A farmer has 2400 feet of fencing to create a rectangular pen for his

lamas next to their new barn. If the barn side off the pen does not

need a fence, what are the dimensions of the pen with the

largest area?


$500$500A = LW = xy

A = 2x + y = 2400

y = 2400 - 2x

A = x(2400 – 2x) = 2400x – 2x2

A’ = 2400 – 4x

X = 600 ft

Y = 1200 ft

A = LW = xy

A = 2x + y = 2400

y = 2400 - 2x

A = x(2400 – 2x) = 2400x – 2x2

A’ = 2400 – 4x

X = 600 ft

Y = 1200 ftHome


$100$100

List the antiderivatives for the following trig functions

Sin Cos Tan

List the antiderivatives for the following trig functions

Sin Cos Tan


$100$100

-cos, sin, sec2-cos, sin, sec2

Home


$200$200

Evaluate the integral

∫ (4 + 3x2) dx

Evaluate the integral

∫ (4 + 3x2) dxo

2


$200$200

1010

Home


$300$300

When is it good to use implicit differentiation?

When is it good to use implicit differentiation?


$300$300

When an equation can not be easily solved for y in terms of x.

When an equation can not be easily solved for y in terms of x.

Home


$400$400

Complete the statement.

Lim [ f(x) + c(g(x))] =

Lim f(x) + ________________

Complete the statement.

Lim [ f(x) + c(g(x))] =

Lim f(x) + ________________x → a

x → a


$400$400

+ c Lim g(x)+ c Lim g(x)

Home

x → a


$500$500

In words, state the product rule and the quotient rule.

In words, state the product rule and the quotient rule.


$500$500Product rule: first time the

derivative of the second + second time the derivative of the first.

Quotient rule: bottom time the derivative of the top – top times the derivative of the bottom all divided by the bottom squared.

Product rule: first time the derivative of the second + second

time the derivative of the first.

Quotient rule: bottom time the derivative of the top – top times the derivative of the bottom all divided by the bottom squared.

Home


Home

CalculusCalculus

Final Jeopardy Question



y = 2π4


y = 2π4


y’ = 0y’ = 0

Home

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