2.3 - Example 4 is the hardest one. Trick : v depends on x...

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Section 2.3 General comments As I mentioned in class, this section is the hardest in Chapter 2. Pay special attention to the 4 examples. You only need to glance through the discussion preceding them on pp. 50 52. Read Example 2 frst. Two types oF model: continuous compounding, com- pounding at fnite time intervals, Former one always better yield than latter one. Equation (15) models a more general situation oF the continuous compounding. Proceed to read Example 1 and 3. They are basically oF the same type. Important steps : ±uid volume constant, thus same amount in, same amount out. Concentration, then determine the rate out.
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Unformatted text preview: Example 4 is the hardest one. Trick : v depends on x , rather than t . Know why (30) has signs, due to the Fact that the positive x-axis points away From the center oF the earth. Think about the reasoning behind Equations (31) (33) careFully. Examples from 9th ed. book 4. (a) dQ dt = 3 2 Q 200+ t initial value Q (0) = 100 (b) concentration Q 200+ t 6. (a) conservation oF energy (b) dV dt = a 2 gh V ( h ) = h A ( u ) du 26. (a) m dv dt = mg kv (b) LHospitals rule 29. (a) m dv dt = G Mm ( R + x ) 2 g = GM R 2 = 78545mi/hr 2 (b) dx dt = v 1...
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