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1. A savings deposit is a medium of exchange. 2. A marketable nancial instrument can be traded on a secondary market. 3. The banking system s ability to issue check-writing deposits is limited by the reserve requirement on checking deposits and the amount of reserves held by the bank. 4. The maximum increase in check-writing deposits is $100,000, ceteris paribus, when the Fed purchases government securities valued at $10,000 and the reserve requirement is 10 percent. 5. When there is a stable demand-for-money curve, a decrease in the M1 money supply lowers the short-term nominal rate of interest. 6. Bank reserves increase and the fed funds rate decreases when the Fed purchases government securities, ceteris paribus. Answers: 1. False; 2. True; 3. True; 4. True; 5. False; 6. True

That call returns to where the second recursive call had left off at line 12. Since that is the last executable statement in the method, it also returns, back to where the first recursive call had left off at line 10. So it proceeds to line 11 with n = 3, x = 'A', y = 'B', and z = 'C'. That prints the fourth line of output:

Then line 12 executes, passing 2 to n, 'B' to x, 'A' to y, and 'C' to z. That call, HanoiTowers(2, 'B', 'A', 'C'), recursively moves the stack of two disks from peg B to to peg C via peg A and generates the last three lines of output:

Move top disk from peg B to peg A. Move top disk from peg B to peg C. Move top disk from peg A to peg C.

Since the previous four moves had already transferred the largest disk from peg A to peg C, this completes the task.

MUTUAL RECURSION When a function calls itself, it is called direct recursion. Another form of recursion is when a function calls other functions that call other functions that eventually call the original function. This is called indirect recursion. Its most common form is when two functions call each other. This is called mutual recursion. (See Figure 9.6.)

b Is there backing for coins, paper currency, and check-writing deposits c How can money have value without commodity backing Solution: a In most cases, one can pay for the purchase of a good or service with cash or by writing a check Since checks are accepted as payment, they are classi ed as money along with coins and paper currency b In the US, coins, paper currency, and checking accounts have no intrinsic value While coins have a metallic content, the market value of the coined material is considerably less than the face (monetary) value of the coin Paper currency is issued by the Fed and has no commodity backing, while check-writing deposits are noncollateralized liabilities of deposit institutions c Anything has value when its supply is limited and demand is virtually unlimited.

The sine and cosine functions from trigonometry can be defined in several different ways, and there are several different algorithms for computing their values. The simplest (although not the most efficient) is via mutual recursion. It is based upon the identities: sin2 = 2sin cos cos2 = 1 2(sin )2 and the two Taylor polynomials: sin x x x 3/6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

public class TestMutualRecursion { public static void main(String[] args) { String fmt1 = "%18s%18s%18s%n"; String fmt2 = "%18.13f%18.13f%18.13f%n"; System.out.printf(fmt1, "s(x) ", "Math.sin(x) ", "error "); for (double x = 0.0; x < 1.0; x += 0.1) { System.out.printf(fmt2, s(x), Math.sin(x), Math.sin(x) - s(x)); } System.out.printf(fmt1, "c(x) ", "Math.cos(x) ", "error "); for (double x = 0.0; x < 1.0; x += 0.1) { System.out.printf(fmt2, c(x), Math.cos(x), c(x) - Math.cos(x)); } } public static double s(double x) { if (-0.005 < x && x < 0.005) { return x - x*x*x/6; // basis } return 2*s(x/2)*c(x/2); // recursion } public static double c(double x) { if (-0.005 < x && x < 0.005) { return 1.0 - x*x/2; // basis } return 1 - 2*s(x/2)*s(x/2); // recursion } }

The output is: