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Chapter 9 Quiz Solutions

# Chapter 9 Quiz Solutions - Chapter 9 Quiz Sec 1 1 Plot the...

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Chapter 9 Quiz Sec. 1 1. Plot the polar curve r ( θ ) = 1 + cos( θ ), 0 θ 2 π . Solution: M FFFFFFFF 11 Π 12 M FFFFFF 5 Π 6 M FFFFFF 3 Π 4 M FFFFFF 2 Π 3 M FFFFFF 7 Π 12 M FFF Π 2 M FFFFFF 5 Π 12 M FFF Π 3 M FFF Π 4 M FFF Π 6 M FFFFF Π 12 0 FFFFF Π 12 FFF Π 6 FFF Π 4 FFF Π 3 FFFFFF 5 Π 12 FFF Π 2 7 Π 12 2 Π 3 3 Π 4 5 Π 6 FFFFFFFF 11 Π 12 Π M 2 M 1 1 2 M 2 M 1 1 2 2. Let ( x ( t ) , y ( t )) parametrize a curve in the plane. Explain why dy dx = y ( t ) x ( t ) . (That is, why is this true?) Solution: There are several reasons why this is true. Here are two. Reason #1. The velocity vector ( x ( t ) , y ( t )) is tangent so it has the same slope as the tangent line. Its slope is rise/run = (y-component)/(x-component) = y ( t ) /x ( t ). Reason #2. Let f be a function whose graph coincides with the parametrized cirve. Then y ( t ) = f ( x ( t )). By the chain rule it follows that y ( t ) = f ( x ( t )) * x ( t ) . Therefore f ( x ) = y ( t ) x ( t ) where x = x ( t ).

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Chapter 9 Quiz Solutions - Chapter 9 Quiz Sec 1 1 Plot the...

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