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Jeopardy Directions for the game: 1. You will need a pencil and paper to keep score.

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Jeopardy

Directions 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

Applications

Other stuff

Limits

Integrals

Misc.

Final Jeopardy

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Scores

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$100

Calculate the derivative of

ex

$100

ex

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$200

Calculate the derivative of

f(x) = x sin (x)

$200

f’(x) = x cos (x) + sin (x)

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$300

Calculate the derivative of

Y = X2(X- 2)5

$300

y’ = 5x2(x-2)4 + (x-2)5(2x)

y’ = x(x-2)4(7x-4)

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$400

Use Implicit Differentiation to calculate y’

X2 + XY + Y3 = 3

$400

2x + xy’ + y + 3y2 y’ = 0

y’ = -2x – y

X + 3y2

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$500

Find the derivative of the following function

F(x) = x3 – 3x2 + 4

x2

$500

y’ = x3-8

x3

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$100

Evaluate

Lim 6X - 3

X → 4

$100

21

Home

$200

Evaluate

Lim sin x

x

X → 0

$200

1

Home

$300

Evaluate

Lim l x – 4 l

x - 4

X → 4

$300

No limit

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$400

Evaluate

Lim X2 – 9

X + 3

X → - 3

$400

-6

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Daily

Double

$500

Evaluate

Lim (X + ΔX)2 + 1 – (X2 + 1)

ΔX

ΔX → 0

$500

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 X

Δ X = 0

Answer = 2X.

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$100

Evaluate

∫ 2x dx

$100

x2 + c

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$200

Evaluate

∫ x3 + 2x

x

$200

1/3 x3 +2x + c

(cancel one x and then integrate)

Home

$300

Evaluate

∫ (lnx)3dx

x

$300

Let U = Lnx, du = 1/x dx

= ¼ (ln x)4 + c

Home

$400

Evaluate

∫ cos 2x dx

$400

½ sin(2x) + c

Home

$500

Evaluate

∫xe-x2 dx

$500

Let u = -x2, du = -2x

-½ ∫ eu du

-½ e-x2+c

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$100

In an application problem relevant to motion, the first derivative of an equation tells ____________.

$100

Velocity

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$200

In an application problem relevant to motion, the second derivative tells ______________.

$200

Acceleration

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$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?

$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

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$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?

$400

1/(25π) cm/s

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$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?

$500

- 78 mi/h

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$100

Find the derivative of

y = ln(x3 + 1)

$100

y’ = 3x2

X3+ 1

Home

$200

Find the derivative of

y = 6(x2)

$200

y’ = (ln 6)(6^x^2)(2x)

Home

$300

Find the second derivative of

y = x3 + 3x2 – ½ x + 5

$300

y = x3 + 3x2 – ½ x + 5

y’ = 3x2 + 6x – ½

y” = 6x + 6

Home

$400

Find y’

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

$400

y’ = lnx +2ln(1+x)

y’ = 1/x +2/(1+x)

Home

$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?

$500

A = LW = xy

A = 2x + y = 2400

y = 2400 - 2x

A = x(2400 – 2x) = 2400x – 2x2

A’ = 2400 – 4x

X = 600 ft

Y = 1200 ft

Home

$100

List the antiderivatives for the following trig functions

SinCosTan

$100

-cos, sin, sec2

Home

$200

Evaluate the integral

∫ (4 + 3x2) dx

2

o

$200

10

Home

$300

When is it good to use implicit differentiation?

$300

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

Home

$400

Complete the statement.

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

Lim f(x) + ________________

x → a

x → a

$400

+ c Lim g(x)

x → a

Home

$500

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

$500

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.

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Final

Jeopardy

Calculus

Final Jeopardy Question

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Calculate the derivative of

y = 2π4

y’ = 0

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