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A: #7
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- find the differential d(e5x + x5)Why is e^x selected as u and not e^2x (to get du /2 = e^x dx in the problem attached?A 200-gal tank is half full of distilled water.At time t = 0, a solution containing 0.5 lb / gal of concentrate entersthe tank at the rate of 5 gal/ min, and the well-stirred mixtureis withdrawn at the rate of 3 gal / min. At what time will the tank be full?
- Is there a way to solve this w/o using L'Hospital's rule?Let the rate of growth dN/dt of a colony of bacteria be proportional to the square root of the number present at any time. If there are no bacteria present at t = 0, how many are there at a later time? Observe here that the routine separation of variables solution gives an unreasonable answer, and the correct answer, N ≡ 0, is not obtainable from the routine solution. (You have to think, not just follow rules!)
