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\fA silver dollar is dropped from the top of a building that is 1331 feet tall. Use the position function below for free-falling objects. s(t) = -16tz + Vot + So (a) Determine the position and velocity functions for the coin. s(t) = V(t ) = (b) Determine the average velocity on the interval [3, 4]. ft/s (c) Find the instantaneous velocities when t = 3 seconds and t = 4 seconds. V ( 3 ) = ft/s V(4) = ft/s (d) Find the time required for the coin to reach the ground level. (Round your answer to three decimal places.) t = (e) Find the velocity of the coin at impact. (Round your answer to three decimal places.) ft/s[dentlfy the real numbers X0, X1, x2, X3 and X4 in the figure such that each of the following is true. (Select all that apply.) none of these (l2) f"[x) = 0 none of these (c) f'(x) does not exist. OXO O X 1 O X 2 O X 3 O X 4 O none of these (d) f has a relative maximum. OXO O X 1 O X 2 O X 3 O X 4 O none of these (e) f has a point of inflection. Oxo O X 1 O X 2 O X 3 O X 4 O none of theseFind an equation of the tangent line to the graph of the function at the given point. y = x2e\" 2xe" + 2e\Find the particular solution of the differential equation that satisfies the initial condition(s). f'(s) = 145 - 45, f(3) = 9 f( s) =Analyze and sketch a graph of the function. Find any intercepts, relative extrema, and points of inflection. (Order your answers from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE.) f( x ) = XV9 -x2 intercepts ( x, y ) = ( x , y ) = ( x, y ) = relative minimum ( x, y ) = relative maximum ( x, y ) = point of inflection ( x, y ) = Find the equations of the asymptotes. (Enter your answers as a comma-separated list of equations. If an answer does not exist, enter DNE.) Use a graphing utility to verify your results. 5- -6 -4 -2 2 4 6 -6 -4 -2 4 -5/ -5/ O OFind the equations of the asymptotes. (Enter your answers as a comma-separated list of equations. If an answer does not exist, enter DNE.) Use a graphing utility to verify your results. -6 W X -4 - 2 2 4 -6 -4 - X -2 4 -5 -5 O O 4 5- -6 -4 - X -2 4 -6 -4 2 2 4 6 -51 -5 O OThe velocity of an automobile starting from rest is given by the equation below, where v is measured in feet per second and r is the time in seconds. (Round your answers to three decimal places.) (a) Find the acceleration at 5 seconds. Ewe (b) Find the acceleration at 10 seconds. |:l Wsecz (c) Find the acceleration at 20 seconds. Ewe A cylindrical package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 117 inches. Find the dimensions of the package of maximum volume that can be sent. (The cross section is circular.) radius In length InFind the area of the region bounded by the graphs of the equations. y =-x -+8x, y=0