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Differential Calculus By: Madison Walters
JeopardyDefinition of a Derivative
Differentiability and Continuity
Tangent LinesVs.
Normal Line
Average Rate of Change
Instantaneous Rate of Change
Q $100
Q $200
Q $300
Q $400
Q $500
Q $100 Q $100Q $100 Q $100
Q $200 Q $200 Q $200 Q $200
Q $300 Q $300 Q $300 Q $300
Q $400 Q $400 Q $400 Q $400
Q $500 Q $500 Q $500 Q $500
Final Jeopardy
$100 QuestionDefinition of a Derivative
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$100 AnswerDefinition of a Derivative
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$200 Question Definition of a Derivative
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$200 AnswerDefinition of a Derivative
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$300 Question Definition of a Derivative
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$300 Answer Definition of a Derivative
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$400 Question Definition of a Derivative
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$400 Answer Definition of a Derivative
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$500 Question Definition of a Derivative
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$500 Answer Definition of a Derivative
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$100 Question Differentiability and Continuity
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$100 Answer Differentiability and Continuity
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$200 Question Differentiability and Continuity
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$200 Answer Differentiability and Continuity
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$300 Question Differentiability and Continuity
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$400 Question Differentiability and Continuity
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$400 Answer Differentiability and Continuity
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$500 Question Differentiability and Continuity
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$500 Answer Differentiability and Continuity
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$100 Question Tangent Lines vs. Normal Lines
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$100 Answer Tangent Lines vs. Normal Lines
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$200 Question Tangent Lines vs. Normal Lines
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$200 Answer Tangent Lines vs. Normal Lines
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$300 Question Tangent Lines vs. Normal Lines
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$400 Question Tangent Lines vs. Normal Lines
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$400 Answer Tangent Lines vs. Normal Lines
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$500 Question Tangent Lines vs. Normal Lines
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$500 Answer Tangent Lines vs. Normal Lines
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$100 QuestionAverage Rate of Change
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$100 Answer Average Rate of Change
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$200 Question Average Rate of Change
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$200 Answer Average Rate of Change
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$300 Question Average Rate of Change
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$400 Question Average Rate of Change
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$400 Answer Average Rate of Change
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$500 Question Average Rate of Change
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$500 Answer Average Rate of Change
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$100 Question Instantaneous Rate of Change
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$100 Answer Instantaneous Rate of Change
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$200 Question Instantaneous Rate of Change
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$200 Answer Instantaneous Rate of Change
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$300 Question Instantaneous Rate of Change
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$300 Answer Instantaneous Rate of Change
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$400 Question Instantaneous Rate of Change
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$400 Answer Instantaneous Rate of Change
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$500 Question Instantaneous Rate of Change
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$500 Answer Instantaneous Rate of Change
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Final JeopardyThe rate of consumption of cola in the US is given by
S(t)=Ce^kt, where S is measured in billions of gallons per year and t is measured in years from the beginning of
1980. The consumption rate doubles every S years and the consumption rate at the beginning of 1980 was 6 billion gallons per year. This is the Av. ROC of cola over the 10
year period beginning January 1, 1983. (Indicate units of measure.)
Final Jeopardy Answer
What is Av. ROC
=(1/13-3) ∫313 6e^((ln2/5)t) dt
=3/ln2 [e^(2.6ln2)-e^(.6ln2)] billion gal/year
=19.680 billion gal/year
