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


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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

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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

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!

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

Derivatives

Applications

Other stuff

Limits

Integrals

Misc.

Final Jeopardy

$100

$100

$100

$100

$100

$100

$200

$200

$200

$200

$200

$200

Scores

$300

$300

$300

$300

$300

$300

$400

$400

$400

$400

$400

$400

$500

$500

$500

$500

$500

$500


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$100

Calculate the derivative of

ex


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$100

ex

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$200

Calculate the derivative of

f(x) = x sin (x)


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$200

f’(x) = x cos (x) + sin (x)

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$300

Calculate the derivative of

Y = X2(X- 2)5


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$300

y’ = 5x2(x-2)4 + (x-2)5(2x)

y’ = x(x-2)4(7x-4)

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$400

Use Implicit Differentiation to calculate y’

X2 + XY + Y3 = 3


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$400

2x + xy’ + y + 3y2 y’ = 0

y’ = -2x – y

X + 3y2

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$500

Find the derivative of the following function

F(x) = x3 – 3x2 + 4

x2


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$500

y’ = x3-8

x3

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$100

Evaluate

Lim 6X - 3

X → 4


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$100

21

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$200

Evaluate

Lim sin x

x

X → 0


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$200

1

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$300

Evaluate

Lim l x – 4 l

x - 4

X → 4


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$300

No limit

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$400

Evaluate

Lim X2 – 9

X + 3

X → - 3


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$400

-6

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

Daily

Double


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$500

Evaluate

Lim (X + ΔX)2 + 1 – (X2 + 1)

ΔX

ΔX → 0


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$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.

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$100

Evaluate

∫ 2x dx


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$100

x2 + c

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$200

Evaluate

∫ x3 + 2x

x


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$200

1/3 x3 +2x + c

(cancel one x and then integrate)

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$300

Evaluate

∫ (lnx)3dx

x


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$300

Let U = Lnx, du = 1/x dx

= ¼ (ln x)4 + c

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$400

Evaluate

∫ cos 2x dx


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$400

½ sin(2x) + c

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$500

Evaluate

∫xe-x2 dx


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$500

Let u = -x2, du = -2x

-½ ∫ eu du

-½ e-x2+c

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$100

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


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$100

Velocity

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$200

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


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$200

Acceleration

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$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?


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$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

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$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?


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$400

1/(25π) cm/s

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$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?


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$500

- 78 mi/h

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$100

Find the derivative of

y = ln(x3 + 1)


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$100

y’ = 3x2

X3+ 1

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$200

Find the derivative of

y = 6(x2)


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$200

y’ = (ln 6)(6^x^2)(2x)

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$300

Find the second derivative of

y = x3 + 3x2 – ½ x + 5


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$300

y = x3 + 3x2 – ½ x + 5

y’ = 3x2 + 6x – ½

y” = 6x + 6

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$400

Find y’

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


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$400

y’ = lnx +2ln(1+x)

y’ = 1/x +2/(1+x)

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$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?


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$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


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$100

List the antiderivatives for the following trig functions

SinCosTan


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$100

-cos, sin, sec2

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$200

Evaluate the integral

∫ (4 + 3x2) dx

2

o


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$200

10

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$300

When is it good to use implicit differentiation?


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$300

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

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$400

Complete the statement.

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

Lim f(x) + ________________

x → a

x → a


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$400

+ c Lim g(x)

x → a

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$500

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


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

$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.

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

Final

Jeopardy

Calculus

Final Jeopardy Question

Home


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

Calculate the derivative of

y = 2π4


Jeopardy directions for the game 1 you will need a pencil and paper to keep score

y’ = 0

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