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Unformatted text preview: f ( x ) = 100-x 2 on [-10 , 10 ] but what geometric gure does it represent? If a population of geese is changing at a rate of 100-t 2 geese per year, where t is the time (in years) from the present, then what will be the growth in population over the next ten years? (Use the geometry to evaluate the integral.) 3. A machine part oscillates back and forth in a straight line with acceleration function given by ( t ) = cos(2 t )-sin( t ) m/s 2 , where t is the time elapsed in seconds. If its initial velocity is 1 m/s, write a formula for its velocity at time t . On what subinterval(s) of [ 0 , 2 ] is the velocity positive? negative? (Use the trigonometric identity sin(2 t ) = 2 sin( t ) cos( t ) and remember that-1 sin( t ) 1 .) Find both the displacement and total distance traveled by the part on the time interval [ 0 , 2 ] by applying Net Change Theorem....
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