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AP Calculus AB / Mr. Hansen |
Name: ____________________________ |
CFU (Check for Understanding) on Chapter 7
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Part II. |
Free response, calculator
required. |
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The town of Originville (located at (0, 0)) is being menaced by a
hurricane currently located at (–2, –1.7). Storms in this part of the world
usually observe the differential equation dy/dx
= (y + 2)2e–x/4. |
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(a) |
Sketch the slope field in
the nearby region, [–3, 3] ´ [–3, 3]. |
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(b) |
Sketch the particular
solution. Does the storm hit Originville? If not,
by about how many units does the storm miss? |
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(c) |
Show your work and use
Euler’s Method to predict the storm’s position when x = –1.4. Use a step size of 0.2 units. |
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(d) |
Now solve the differential
equation and compute the storm’s position as predicted by an exact solution.
Explain any discrepancy with part (c). |