# Calculus

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After Lee gives his little sister Kara a big push on a swing, her horizontal position as a function of time is given by the equation x(t)= 3cost(e^-0.05t), where x(t) is her horizontal displacement, in metres, from the lowest point of her swing, as a function of time, t, in seconds.

a) From what horizontal distance feom the bottom of Kara's swing did Lee push his sister.
B) Determine the greatest speed Kara will reach and when this occurs.
C) How long will it take for Kara's max horizontal displacement at the top of her swing arc to diminish to 1 m?

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