27 - Tangents velocities other rates of change given a...

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Unformatted text preview: Tangents, velocities, other rates of change given a curve and a point on the graph, the slope tangent line to the curve at is given by lim given that the position of an object moving in a line at time is given by then the average velocity from to is given by , of the and the instantaneous velocity at lim If is given by is any function, then we define the change in , denoted by is denoted by or and is , to be Then the corresponding change in and then the instantaneous rate of change is given by lim lim MTH 173, section 2.7, page 1 if position function is , a. write average velocity from to b. instantaneous velocity at lim lim lim determine slope of tangent to lim lim lim then equation of this tangent the slope is and goes thru lim at lim , so, using , we have then graph both until they coincide MTH 173, section 2.7, page 2 these almost coincide determine slope of tangent to lim lim lim lim at determine slopes when Now we just evaluate the slope function eqn: eqn: eqn: graph function and these tangents. at these values MTH 173, section 2.7, page 3 sketch position against time velocity after one second lim lim MTH 173, section 2.7, page 4 lim velocity when lim lim lim lim m/s lim This result is a function that we can use to determine velocity of the object at any time . when will hit moon (i.e., when will ) seconds with what velocity will hit moon? To determine this, we can evaluate the velocity function we determined in part b at the time obtained in part c: m/s If is any function, then we define the change in , denoted by , to be MTH 173, section 2.7, page 5 Then the corresponding change in is denoted by or and is and then the instantaneous rate of change is given by lim 157-22 I sketch a tangent line at The slope is them and observe it goes thru (approximately) lim MTH 173, section 2.7, page 6 ...
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This note was uploaded on 09/17/2009 for the course MTH Calc taught by Professor Bush during the Fall '09 term at Northern Virginia.

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