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1.The motion of a spring that is subject to a frictional force or a damping force (such as a shock absorber in a car) is often modeled by the product of an exponential function and a sine or cosine function. Suppose the equation of motion of a point on such a spring is
s(t) = 4e−1.9t sin 2πt
where
s is measured in centimeters and
t in seconds. Find the velocity after
t seconds.
2.Find the x-coordinates of all points on the curve
f(x) = sin 2x − 2 sin x
at which the tangent line is horizontal. (Enter your answers as a comma-separated list. Use
n to represent any integer.)
3.ind an equation of the tangent line to the curve at the given point.
y = sin 9x + sin2 9x,(0, 0)
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