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FinalFR2006

# Calculus: Early Transcendental Functions

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Free Response Final 2006 Name 1. Consider the differential equation dy ccccccc dx = 2 x cccccccc y H A L On the axes provided below, sketch a slope field for the given differential equation at the 15 points indicated, and sketch the solution curve that passes through the point H 0, 2 L . 1 2 2 3 4 5 H B L Using the differential equation above, dy ccccccc dx = 2 x cccccccc y , and Euler s method starting at f H 0 L = 2, and a step size H x L of 1, calculate f H 2 L H take two steps L . H C L Now, solve the differential equation dy ccccccc dx = 2 x cccccccc y where y H 0 L = 2. What type of curve is this?

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2. Wow, it s getting cold all of a sudden ! Below is a table of temperatures taken outside the Monta Vista main office on Monday morning. Time H t L 6 am 7 am 8 am 9 am 10 am 11 am 12 pm Temperature H in degrees Celsius L 3 7 10 12 14 15 16 H A L If we assume that the temperature during the 6 hour period can be modeled by a differentiable function W H t L , approximate W H 8 L , and indicate units of measure.
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