Differential Equations

2. Find and graph all nullclines and find all equilibrium points for the system r² = 8r - 2x² - ry y = 6y-xy-y² Draw the h nullclines as dashed curves and the v nullclines as solid curves. 023 er

1. Use limits involving to describing the asymptotic behavior of each function from its graph. 3x x-2 f(x) =

2. Find the derivative of the following function: f(x) = 4√x³-—+1

5. Graph the following function showing all relative extreme points and inflection points: f(x) = x³ + 3x² - 9x - 7

6. A computer dealer can sell 12 personal computers per week at a price of $2,000 each. He estimates that each $400 price decrease will result in three more sales per week. If the computers cost him $1,200 each, what price should he charge to maximize his profit? How many will he sell at that price? dy

9. One bank offers 6% compounded quarterly and a second offers 5.98% compounded continuously. Where should you take your money?

12. Evaluate the definite integral of the following: fe ex/2 dx

11. Find the indefinite integral for the following: (12x³ +6 x³ + 6x - 3)dx

14. Find the integral by a substitution or by integration by parts, as appropriate. x³ In2xdx

13. The population of the United States is predicted to be P(t) = 310e0.0073t million, where tis the number of years after 2010. Find the average population between the years 2010 and 2110.