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1. Find a function y(x) with dy/dx = x⁴ and y(0) = 3.

2. Find a function y(x) with dy/dx = x⁴ and y(2) = 3.

3. Find a general solution to df/dx = e^3x.

4. Find a function y(x) with dy/dx = (1/x) + (1/x²) − x² and y(1) = 2.

5. Find a function y(x) with dy/dx = x/(x² + 1) and y(0) = 0.

6. Find a function y(x) with dy/dx = e^−0.03x and y(0) = 17.

7. Find a function y(x) with dy/dx = e^−0.07x and y(0) = 10, 000.

8. Find a function y(x) with dy/dx = e^0.02x and y(0) = 10, 000.

9. Find a function y(x) with dy/dx = 4/(5 − x) and y(0) = 11. For which values of x

is y defined?

10. Find the general solution f(x) to df/dx = (x⁴ + 3)¹⁰³ x³.

11. Find the general solution f(x) to df/dx = x e^{−9x^2}

13. The marginal cost of treating an additional patient at a specialty clinic when p patients are being served is mc = 60 − p + 0.01p². Calculate the total cost of treating p patients, assuming that the fixed cost is 5 million dollars. Notice that the costs are over the life-time of the clinic.

14. The cost of treating patients at a clinic is as above. Calculate the average cost (per patient) of treating p patients. For how many patients is the marginal cost equal to the average cost? (It makes sense to approximate this optimal number with an integer.)

15. Consider the cost of treating patients at a clinic, as above. Denote the number of patients for which marginal cost equals average cost by q. Is it less expensive to treat 2q patients in two clinics each of which treats q patients, or is it less expensive to treat all the patients in one clinic?

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Status NEW Posted 10 Jul 2017 03:07 AM My Price 8.00

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