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(1 point) The displacement of a particle on a vibrating string is given by the equation 50?) = 14 + %sin(121n), where s is measured in centimeters and t in seconds. Find the velocity of the particle after I seconds. 0(1) 2 pi'cos(3*pi't) \f(1 point) Let F(x) = f(f(x)) and G(x) = (F(x))2 and suppose that f(9) = 4, f(4) = 2, f' (4) = 11, f'(9) = 11 Find F' (9) and G' (9). F' (9) = G' (9) =(1 point) At what point does the normal to y = 4 + 3x + 4x2 at (1, 11) intersect the parabola a second time? Answer: Note: You should enter a cartesian coordinate. The normal line is perpendicular to the tangent line. If two lines are perpendicular their slopes are negative reciprocals -- i.e. it the slope of the first line is m then the slope of the second line is 1/m (1 point) Find the equation of the tangent line to the curve y = 2x cos x at the point (7:, 2:r). The equation of this tangent line can be written in the form y = mx + b. Compute m and b. (1 point) Suppose that f ( ) = -3 and f' ( ) = 5, and let g(x) = f(x) sin x and h(x) = COS X Answer the following questions. f (x) 1. Find g' (7/4). Answer: g' (7/4) = 2. Find h' (7/4). Answer: h'(7/4) =