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v1 v2 vn 0 if lim vn 0. Now n!1 n v1 v2 vn v1 v2 vP vP 1 vp 2 vn n n n We must show that lim

2 1 2 1 1 2 1 2 2 1

2 1 1 2 1 2 2 1

4 3 2 1 0 1 2

v 1 v 2 v n @ jv1 v2 vP j jvP 1 j jvP 2 j jvn j n n n Then

1 2 3 4

Note that even though you are granting public access to the resource, you will still want to restrict operation privileges on the share by mapping guest access to a valid UNIX account Indicate the desired user account name as a value to the guest account parameter A.

GraphicsArray[{g1, g2},{ g3, g4}]

1 1 2

jvP 1 j jvP 2 j jvn j =2 =2 =2 n P =2 < < n n n 2 After choosing P we can choose N so that for n > N > P, jv1 v2 vP j < n 2 Then using (2) and (3), (1) becomes v 1 v 2 v n < 2 2 n thus proving the required result.

1 1 2

4 3 2 1

- 150 -

1 1 2 3

Now by the binomial theorem,

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Plot has a variety of options that can be viewed by typing Plot or Options[Plot]. These options may be used individually or in conjunction with one another. Some of the more common options are described in the remainder of this section. Since Mathematica obviously cannot plot an infinite number of points, it selects a finite number of equally spaced points as sample points and uses an adaptive algorithm to construct a smoothlooking curve. The initial number of points it will use, PlotPoints, is set to 50 by default. If the curve wiggles excessively, a larger number might be necessary to obtain a smooth-looking curve.

PlotPoints n specifies that an initial number of n sample points should be used in the construction of the graph. MaxRecursion n specifies that up to n levels of recursion should be made in the adaptive algorithm. Recursive subdivision is done only in those places where more samples seem to be needed in order to achieve results with a certain level of quality.

CHAP. 2]

When you plot a graph, you will notice that the horizontal and vertical axes are usually not the same length. By default, the ratio of vertical axis length to horizontal axis length is 1/GoldenRatio, where GoldenRatio = (1 + 5 ) / 2 . The designers of Mathematica felt that this ratio was the most comfortable and pleasing to the eye. It can be changed with the option AspectRatio, which determines the height-to-width ratio of the graph.

good candidate account with limited privileges is the nobody account which is commonly used for UNIX anonymous access services (Example 11.6). Example 11.6 Restricting Guest Access guest ok = true guest account = nobody

AspectRatio Automatic computes the aspect ratio from the actual coordinate values of the plot. AspectRatio ratio sets the ratio of height to width to the value ratio.

Plot[x2, {x, 5, 5}]

n n 1 2 n n 1 n 2 3 un un un n 2! 3!

Plot[x2, {x, 5, 5}, AspectRatio Automatic]

Now that we've narrowed connection rights down to an explicit community of client users and machines, we'll want to bind the set of operations permitted on file and directory objects contained within the share This is accomplished by indicating whether a user has read or write privileges based on effective UNIX user and group identifiers, and how UNIX owner, group and world permissions are specified for manipulating files and directories Keep in mind that Samba must honor UNIX permissions regardless of the parameter specifications designated for the share in smbconf Read/write permissions can be specified at the share level or user level using the readonly, read list, writeable, and write list parameters If the user name is prefixed with an "@" sign or a "&" sign it is assumed to correspond to an NIS netgroup.

25 20 15 10 5 4 2 2 4 4 2 2 4 5

EXAMPLE 8 The following command should produce a circle of radius 3 centered at the origin. However, because of unequal axis scaling, the graph appears as an ellipse.

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