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

10. If a bank offers 6.5% interest, in how many years will a deposit increase by 50% if the compounding is done: a. Quarterly? b. Continuously?

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

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

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.

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

16. For the function, state the domain of the following: f(x,y) √x

19. Find the derivative of the following function: f(t) = sin(2-3t)

17. For each function f, find: a. fx b. fy C. fxy d. fyx f(x, y) = 2x5 - 3x²y³ + y4 − 3x + 2y +7

18. Sketch the graph of the following function. If you use a graphing calculator, make a hand-drawn sketch showing the amplitude and period.) y = 7cos2x