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Exam Questions 17
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Lucas Standen
.AI
QMC

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1)a)

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dx over dt = 2cos(t)
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dy over dt = 2sin(2t)
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dy over dx = 2cos(t) over 2sin(2t)
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"when " t = pi over 6
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dy over dx = {2cos({pi over 6})} over {2sin(2({pi over 6}))}
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dy over dx = 1
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1)b)

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x = 2sin(t) 
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x over 2 = sin(t)
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1 = cos(2t)
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1 = 1 - cos sup 2 (t)
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y = cos sup 2 (t)
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({x over 2}) sup 2 + y sup 2 = 1
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{x over 4} sup 2 + y sup 2 = 1
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{x over 4} sup 2 - 1 = - y sup 2 
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- {x over 4} sup 2 + 1 = y sup 2 
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sqrt {- {x over 4} sup 2 + 1} = y sup 2 
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-2 <= x <= 2 
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1)c)

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0 <= f(x) <= 1
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