Jeopardy...Yeah!

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Jeopardy...Yeah!
On With the Show
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Welcome to the Jeopardy of Calculus AB. The
questions are based on Chapter 4 Materials.
Jeopardy
Jeopardy
Lets go to the Game Board
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Categories
Area Integration Mental Funds U-Substitution Potpourri
100 100 100 100 100
200 200 200 200 200
300 300 300 300 300
400 400 400 400 400
500 500 500 500 500
Final Jeopardy
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Area 100

• Find the sum.
• Answer

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Answer

• The distributive property of summation says
  that we can place any constant outside of the
  sigma notation.
• Categories

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Area200

• Find the sum.
• Answer

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Answer

• We evaluate this sum by replacing k with 0, then
  1,2,3, and 4 respectively.
• Categories

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Daily Double!!!

• Choose the amount you would like to wager. (Up
  to half your score)

Question
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Area300

• Find a formula for the sum of n terms. Use the
  formula to find the limit as n? infinity.
• Answer

10
Answer

• Evaluate the summation
• After simplifications
• And the answer
• Categories
  

11
Area400

• Determine a value that best approximates the area
  of the x-axis and the graph of the function over
  the indicated interval.
• f(x) 4 x2, 0,2
• Answer

12
Answer

• First sketch a graph of the function
• Then approximate counting the squares
• A11110.50.50.55.5
• Categories

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Area500

• Find the sum
• Answer

14
Answer

• Solve the summation
• Categories

15
Integration100

• Answer

16
Answer

• Integrate each part separately. Dont forget
  the C! Then rewrite to
• Categories

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Integration200

• Answer

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Answer

• Integrate
• Categories

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Integration300

• Answer

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Answer

• First, integrate t2 separately from
• sint. Then integrate sint. (Chain Rule) Then
  rewrite to
• Categories

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Integration400

• Solve the differential equation
• Answer

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Answer

• First, integrate the equation. Then plug in 2 for
  x, and find C. Then rewrite to
• Categories

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Integration500

• Calculate the indefinite integral
• Answer

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Answer

• First divide the entire equation by the x in the
  denominator. Then integrate each piece
  independently of each other.
• Categories

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Mental Funds100

• Find the area of the region bounded by the
  equation
• On the interval 0,2.
• Answer

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Answer

• Categories

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Mental Funds200

• Find the average value of
• On the interval 1,4.
• Answer

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Answer

• Categories

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Mental Funds300

• Evaluate the definite integral
• Answer

30
Answer

• First Expand
• Then Integrate
• Then plug in the Numbers
• Answer
• Categories

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Mental Funds400

• Using the second fundamental theorem of Calculus
  find F(x)
• Answer

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Answer

• Simply plug in x for t.
• Categories

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Mental Funds500

• Using the second fundamental theorem of Calculus
  find F(X)
• Answer

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Answer

• Using chain rule derive the inside and then plug
  in the x3.
• Categories

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U-Substitution100

• Answer

36
Answer

• Thus u 2x du 2dx ½du dx
• ? ½(cosu) ? ½cos2x
• Categories

½cos2x
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U-Substitution200

• Answer

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Answer

• U x21 du 2x dx ½du x dx
• ½ ½
• Categories

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U-Substitution 300

• Answer

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Answer

• Categories

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U-Substitution400

• Answer

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Answer

• Categories

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U-Substitution 500

• Answer

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Answer

• Categories

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Potpourri100

• Derive
• Answer

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Answer

• Categories

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Potpourri 200

• Find the limit
• Answer

48
Answer

• You should know that as x approaches 0 in the
  limit
• The limit equals one.
• Categories

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Potpourri 300

• Derive this equation
• Answer

50
Answer

• Categories

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Potpourri 400

• Integrate
• Answer

52
Answer

• Categories

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Potpourri 500

• Integrate the indefinite Integral
• Answer

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Answer

• Expand
• Integrate
• Answer
• Categories

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Final Jeopardy

• Think about your wager for final Jeopardy!

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• The category is
• The Angle between two Vectors!

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• Just Kidding!
• Your Category is
• Area Approximations!

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Decide wager amount Wager some, all, or nothing
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Use Trapezoid Rule to Approximate
n4
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Solution
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Solution We now use Trapezoid Rule to
approximate the definite integral. Answer
2.0599
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Area!

• Using integration, and arithmetic sums, to
  determine the area produced between the graph and
  the x-axis.

Categories
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Integration!

• Using basic integration to determine both
  definite and indefinite integrals. Dont forget
  the C!

Categories
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Mental Funds!

• Understand the fundamental theorems of calculus
  for this partyoull need them. TRUST ME!

Categories
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U-Sub!

• Using U-Substitution, find the integrals of some
  problems.
• Warningsome of these problems are rather
  difficult!

Categories
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Potpourri!

• Anything and Everything From the Three Previous
  Chapters! HAHAHAHA!
• Solvers Beware!

Categories