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$100 $400 $300$200$400 $200$100$100$400 $200$200$500 $500$300 $200$500 $100$300$100$300 $500$300$400$400$500

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Derivatives

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Integrals

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Tangent Lines

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PVA

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Potpourri

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DerivativesIntegrals PVA Potpourri $100 $300 $200 $400 $500

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Derivatives- $100

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Derivatives - $200

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Derivatives - $300

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Derivatives - $400

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Derivatives- $500

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Integrals - $100

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Integrals - $200

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Integrals - $300

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Integrals - $400

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Integrals - $500

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Tangent Lines - $100 If f (2) = 5 and f '(2) = 3, write the equation of the line tangent to f (x) at x = 2

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Tangent Lines - $200 If the line tangent to f (x) at the point (3, -4) passes through (11, -8), find f '(3)

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Tangent Lines - $300

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Tangent Lines - $400 If f (2) = 3 and f '(2) = -5, And if g(x)=x ·f (x), write the equation of the line tangent to g(x) at x = 2.

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Tangent lines - $500 If f (1) = 4 and f '(1) = 3, use the tangent line to approximate f (1.1). If f ''(1) = 5, determine if your approximation is greater or less than the actual value and state why.

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PVA - $100 If a particle's position is given by x(t) = 2t 3 – 21t 2 + 72t – 53, t ≥ 0, at what time(s) is the particle at rest? State why.

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PVA - $200 If a particle's position is given by x(t) = 2t 3 – 21t 2 + 72t – 53, t ≥ 0, where x is in feet and t is in seconds, what is the particle's acceleration at t = 4? Include units with your answer.

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PVA - $300 If a particle's position is given by x(t) = 2t 3 – 21t 2 + 72t – 53, t ≥ 0, for what values of t is the velocity increasing? State why.

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PVA - $400 If a particle's position is given by x(t) = 2t 3 – 21t 2 + 72t – 53, t ≥ 0, where x is in feet and t is in seconds, what is the particle's average velocity from t = 0 to t = 2? Include units with your answer.

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PVA - $500 Calculator question: A particle's acceleration is given by a(t) = ln(1 + 2 t ). If v(1) = 2, find v(2).

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Potpourri - $100 The radius of a circle is increasing at a constant rate of 5 m/sec. What is the rate of increase in the area of the circle at the moment its circumference is 20π meters?

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Potpourri - $200 ("DNE" will not be accepted)

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Potpourri - $300 find a and b so that f (x) is differentiable at x = 3.

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Potpourri - $400 Calculator question: The base of a solid is the region in the first quadrant bounded by the y-axis, y = tan -1 x, y = 3 and x = 1. If each cross section perpendicular to the x- axis is a rectangle with a height of 4, what is the volume of this solid?

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Potpourri - $500 A population changes at a rate inversely proportional to the square of the population at any given time. If the initial population is 30 and after 10 years it is 300, what is the population after 17 years? (round to the nearest whole number)

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Derivatives- $100 2(x 3 + 1)(3x 2 ) or 6x 2 (x 3 + 1) or 6x 5 + 6x 2

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Derivatives - $200

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Derivatives - $300 -2/5

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Derivatives - $400 sin(x 6 ) ·2 x

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Derivatives - $500 1/4

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Integrals - $100

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Integrals - $200

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Integrals - $300 10

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Integrals - $400

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Integrals - $500

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Tangent Lines - $100 y – 5 = 3(x – 2) or y = 3x – 1

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Tangent Lines - $200 -1/2

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Tangent Lines - $300 4/9

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Tangent Lines - $400 y – 6 = -7(x – 2) or y = -7x + 20

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Tangent Lines - $500 f (1.1) ≈ 4.3 This is less than the actual value because f (x) is concave up

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PVA - $100 At t = 3, t = 4 because the velocity is zero

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PVA - $200 6 ft/sec 2

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PVA - $300 t > 7/2 or (7/2, ∞) because acceleration is positive

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PVA - $400 38 ft/sec

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PVA - $500 3.346

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Potpourri - $100 100π

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Potpourri - $200 ∞

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Potpourri - $300 a = -5/2, b = -11/4

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Potpourri - $400 10.245

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Potpourri - $500 358

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FINAL CATEGORY Riemann Sums

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FINAL CATEGORY Write the definite integral approximated by the Reimann sum shown above. (Hint: this is a right-handed Reimann Sum)

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FINAL CATEGORY

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END OF GAME Daily Doubles and usage notes follow...

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JEOPARDY! Slide Show Notes The font for the question & answer slides is “Enchanted;” a copy of this font in located in the “REAL Jeopardy Template” folder. (This font will need to be installed in the C:/WINDOWS/FONTS folder of the computer running the show.) In order to keep all of the sounds and fonts together, copy the entire “REAL Jeopardy Template” folder. To change the categories: –1. Go to “Edit” and “Replace…” –2. In the Find box, type Factoring (all caps) –3. In the Replace box, type the category in all caps (for example, PRESIDENTS) –4. Click Replace All... To use the Daily Double: –1. Choose which dollar values to set as Daily Double –2. Link that dollar value to one of the DD slides –3. Link the arrow on the DD slide to the correct question slide (so dollar/category match)

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Running the JEOPARDY! Slide Show On the game board with the categories on top, click on the desired dollar value. (The first game board is used only to blink in the dollar values like the show.) ICONS: –? Go to the answer screen. –House Go back to the game board. –Right Arrow (on Daily Doubles) Go to the question screen. –Turned-up Arrow Reload question screen after incorrect guess

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$100 $400 $300$200$400 $200$100$100$400 $200$200$500 $500$300 $200$500 $100$300$100$300 $500$300$400$400$500.

$100 $400 $300$200$400 $200$100$100$400 $200$200$500 $500$300 $200$500 $100$300$100$300 $500$300$400$400$500.

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