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In each domain, one or more Windows NT computers, called domain controllers, act as a locus for administering and resolving access to all the resources located in the domain The Primary Domain Controller (PDC) maintains a directory of all the account, group, and password information for the domain The directory of domain account information is called the Security Accounts Manager (SAM) SAM information may be replicated to one or more Backup Domain Controllers (BDC) Resources may be shared between domains by defining trust relationships Windows 2000 Active Directory technology groups domains into hierarchical topologies called trees and forests Resources within a domain are located via browsing services Each subnet within a domain has an elected local master browser, which maintains a list of available resources within the subnet The domain PDC acts as a domain master browser to synchronize local master browser resource information.

The condition || P || 0 guarantees that the lengths of all subintervals shrink toward 0 as we take more and more subintervals. If all subintervals are of equal length, this condition is equivalent to n . For convenience we shall only consider subintervals of equal length. However, in theory, this need not be the case.

(a) 2 5 3i 3 2 i 5 i 3 , (b) 3 2i 3 2 4i 2 1 i 2 3i 4 2i e f : 5 7i ; 1 2i 2 1 i (d) 1, (e)

good example for comparative purposes. (a) We use 100 subintervals and choose xi* to be the left endpoint of each subinterval. f[x_] = Sin[x]; a = 0; b = /2; n = 100; x = (b a)/n;

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10 37,

xstar[i_] = a + (i 1) x;

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0.992125 (b) We choose the value of xi* to be the right endpoint of each subinterval. (This time we expect an overapproximation.) f[x_] = Sin[x]; a = 0; b = /2; n = 100; x = (b a)/n; xstar[i_]= a + i x;

To improve the accuracy of the approximation offered in Example 16, we can choose the value of xi* to be the midpoint of each subinterval. This leads to an approximation method called the midpoint rule.

2 i, 5

f[x_] = Sin[x] ; a = 0; b = o/2; n = 100; x = (b a)/n;. xstar[i_] = a +(i .5) x;

Another simple approximation method, called the trapezoidal rule, improves accuracy by connecting the points on the curve corresponding to the points of subdivision with line segments, forming trapezoidal approximations of the area in place of rectangular approximations.

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The area enclosed by a trapezoid with base x and sides A and B is x ( A + B). 2 Thus, the area enclosed by the trapezoid constructed in the ith interval, xi [xi 1, xi], is f ( xi 1 ) + f ( xi ) . 2 The total trapezoidal area, obtained by adding the individual areas, is

f (xi 1) f (xi)

HPFS, NTFS, and DFS. The Microsoft Distributed File System (DFS) provides a means of organizing directory shares on multiple computers into a single directory tree. Print devices with an associated printer driver are represented as virtual printer objects and referenced by a queue name. Multiple physical print devices, called a printer pool, may be referenced by a single queue name. The Local Security Authority (LSA) and Net Login service are responsible for verifying access rights to resources and authenticating login requests respectively. Resource permissions are definedby Access Control Lists (ACLs). Windows 2000 enhances the SAM/LSA mechanism by integrating Kerberos 5.0 for network authentication.

2 i. 5

x x x1 x [ f ( x 0 ) + f ( x1 )] + 2 [ f ( x1 ) + f ( x 2 )] + 3 [ f ( x 2 ) + f ( x3 )] + . . . + n [ f ( x n 1 ) + f ( x n )] 2 2 2 2 If all intervals have the same length, x, this reduces to x [ f ( x 0 ) + f ( x1 )] + [ f ( x1 ) + f ( x 2 )] + [ f ( x 2 ) + f ( x3 )] + . . . + [ f ( x n 1 ) + f ( x n )] 2 or x f ( x 0 ) + 2 f ( x1 ) + 2 f ( x 2 ) + 2 f ( x3 ) + . . . + 2 f ( x n 1 ) + f ( x n ) 2

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