course Mth 173 ?J????????G?????assignment #013s?r??????????????Calculus I
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18:10:15 query problem 2.4.6 derivative of fn (poly zeros at -3,1,3.5, neg for pos x)Describe the graph of your function, including all intercepts, asymptotes, intervals of increasing behavior, behavior for large |x| and concavity
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RESPONSE --> This is not problem 2.4.6 in 4th edition.
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18:17:50 ** The x intercepts of the derivative function will occur when the given function levels off, which occurs at approximately x = -1.5 and at x = 2.5. Between these x values the function is increasing so the derivative will be positive. Every where else the function is decreasing so the derivative will be negative. The derivative will take its greatest positive value where the original graph has its steepest upward slope, which probably occurs around x = .5. As x approaches +infinity the steepness of the original graph approaches -infinity so the value of the derivative function approaches -infinity. As x approaches -infinity the steepness of the original graph approaches -infinity so the value of the derivative function approaches -infinity. This description would be satisfied, for example, by a parabola opening downward, with vertex above the x axis around x = .5. **
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RESPONSE --> Ok.
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18:20:10 query problem 2.4.37 . Which graph matches the graph of the bus and why?
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RESPONSE --> Looks to be problem 2.3.35(a) in 4th edition. I believe it is Graph II. This is because the graph has a series of regular humps of a uniform size. This would indicate stop-and-go motion of the vehicle, which the bus certainly does.
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18:20:20 ** The bus only makes periodic stops, whereas the graph for III only comes to a stop once. I would matche the bus with II. **
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RESPONSE --> Ok.
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18:20:48 describe the graph of the car with no traffic and no lights
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RESPONSE --> This would be graph I, in which there is only one increase in speed and no stops.
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18:20:54 ** The car matches up with (I), which is a continuous, straight horizontal line representing the constant velocity of a car with no traffic and no lights. *&*&
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RESPONSE --> Ok.
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18:21:48 describe the graph of the car with heavy traffic
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RESPONSE --> This would be graph III, since the car in heavy traffic would speed up and slow down to match the speed of other vehicles. These speed increases and decreases would be irregular.
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18:21:54 ** The car in heavy traffic would do a lot of speeding up and slowing down at irregular intervals, which would match the graph in III with its frequent increases and decreases. **
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RESPONSE --> Ok.
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18:22:54 query 2.5.10 (was 2.4.8) q = f(p) (price and quantity sold)what is the meaning of f(150) = 2000?
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RESPONSE --> This looks to be problem 2.4.10. This means that at a cost of $150, 2000 units would be sold.
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18:22:59 *&*& q = 2000 when p = 150, meaning that when the price is set at $150 we expect to sell 2000 units. *&*&
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RESPONSE --> Ok.
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18:24:10 what is the meaning of f'(150) = -25?
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RESPONSE --> This is the rate at which units sold varies with cost. At this point it means that for every $1 of cost increase, 25 units units would not be expected to sell.
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18:24:19 ** f' is the derivative, the limiting value of `df / `dp, giving the rate at which the quantity q changes with respect to price p. If f'(150) = -25, this means that when the price is $150 the price will be changing at a rate of -25 units per dollar of price increase. Roughly speaking, a one dollar price increase would result in a loss of 25 in the number sold. **
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RESPONSE --> Ok.
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18:28:08 query problem 2.5.18 graph of v vs. t for no parachute. Describe your graph, including all intercepts, asymptotes, intervals of increasing behavior, behavior for large |t| and concavity, and tell why the graph's concavity is as you indicate.
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RESPONSE --> 4th edition problem 2.4.18. My graph is a continuous line (up to the point of impact). There are no intercepts in this graph. In the interval from the starting point to the terminal velocity, the graph is concave down, increasing at a decreasing rate. As the person's speed approaches terminal velocity, the change in speed becomes less and less until it disappears. At large |t|, the graph is a straight line (unless the person has met the ground).
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18:28:56 ** When you fall without a parachute v will inrease, most rapidly at first, then less and less rapidly as air resistance increases. When t = 0 we presume that v = 0. The graph of v vs. t is therefore characterized as an increasing graph beginning out at the origin, starting out nearly linear (the initial slope is equal to the acceleration of gravity) but with a decreasing slope. The graph is therefore concave downward. At a certain velocity the force of air resistance is equal and opposite to that of gravity and you stop accelerating; velocity will approach that 'terminal velocity' as a horizontal asymptote. The reason for the concavity is that velocity increases less and less quickly as air resistance increases; the approach of the velocity to terminal velocity is more and more gradual **
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RESPONSE --> Ok. I missed the horizontal asymptote, which makes sense. Always approaching, never able to actually get there.
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18:29:15 What does the t = 0 acceleration indicate?
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RESPONSE --> That acceleration is roughly the same as that of gravity.
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18:29:27 ** t = 0 acceleration is acceleration under the force of gravity, before you build velocity and start encountering significant air resistance. Acceleration is rate of velocity change, indicated by the slope of the v vs. t graph. **
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RESPONSE --> Ok.
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18:29:46 Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> I need to remember horizontal asymptotes.
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