Bc Fiesta 4web
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AP CALCULUS BC | FIESTA 4 | FALL 2008 | SHUBLEKA
NAME__________________________ Problem 1 Wataru sprints around a circular track of radius 100 m at a constant speed of 7 m/s. Mitsu, who is Wataru’s friend, is standing at a distance 200 m from the center of the track. How fast is the distance between the friends changing when the distance between them is 200m? Problem 2 If appropriate, use L’Hopital’s Rule to determine the limit. If not appropriate, explain why and use other methods: x lim arcsin = x x→0
lim ln lnx x = x→∞
Problem 3 * Suppose that three points on the parabola f ( x) = x 2 have the property that their normal lines intersect at a common point. Show that the sum of their x-coordinates is zero.
NAME__________________________ Problem 1 Wataru sprints around a circular track of radius 100 m at a constant speed of 7 m/s. Mitsu, who is Wataru’s friend, is standing at a distance 200 m from the center of the track. How fast is the distance between the friends changing when the distance between them is 200m? Problem 2 If appropriate, use L’Hopital’s Rule to determine the limit. If not appropriate, explain why and use other methods: x lim arcsin = x x→0
lim ln lnx x = x→∞
Problem 3 * Suppose that three points on the parabola f ( x) = x 2 have the property that their normal lines intersect at a common point. Show that the sum of their x-coordinates is zero.
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