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If f x 2x2 , 0 < x @ 2, nd (a) the l.u.b. and (b) the g.l.b. of f x . Determine whether f x attains its l.u.b. and g.l.b. Ans. (a) 8, (b) 0 Construct a graph for each of the following functions. a b f x jxj; 3 @ x @ 3 f x 2 jxj ; 2 @ x @ 2 x x<0 x 0 x>0 f g x x where x greatest integer @ x x f x cosh x

dataset = {1.5, 3, 4.5, 9}; g1 = PieChart[dataset]; g2 = PieChart[dataset, SectorSpacing {Tiny, None}]; GraphicsArray[{g1, g2}]

datalist = {1.5, 3, 4.5, 9}; g1 = PieChart[datalist, ChartLabels {"First Sector", "Second Sector", "Third Sector", "Fourth Sector"}]

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primelist = Table[Prime[k], {k, 1, 50}]; ListPlot[primelist]

x; 2 @ x @ 0 x; 0@x@2

200 150 100 50

list = {{0, 0}, {2, 7}, {3, 5}, {4, 11}}; ListLinePlot[list, PlotMarkers Automatic]

10 8 6 4 2

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represents any valid UNIX command or shell script combination. The parameter string value is passed to C library system() routine which then forks and executes sh (command language interpreter) to parse and execute the passed string. The command string value will likely include instances of Samba substitution variables (Table 12.2). Variable values will be resolved before passing the string to the system() routine. It is a good idea to use the full path name for any command or script in a command parameter value. This avoids problems associated resolving paths during execution. Sample command strings are listed in Example 12.3. Table 12.2 Printer Share Substitution Variables

4.20 Plot the set of points corresponding to the first ten primes, the first ten Fibonacci numbers, and the first ten perfect squares. First plot individual points and then plot them connected with line segments.

PlotLegends` list1 = Table[Prime[n], {n, 1, 10}]; list2 = Table[Fibonacci[n], {n, 1, 10}]; list3 = Table[n2, {n, 1, 10}]; ListPlot[{list1, list2, list3}, PlotMarkers Automatic, PlotLegend {"Primes", "Fibonacci", "Squares"}, LegendPosition {1,0}]

Construct graphs for (a) x2 =a2 y2 =b2 1, (b) x2 =a2 y2 =b2 1, (c) y2 2px, and (d) y 2ax x2 , where a; b; p are given constants. In which cases when solved for y is there exactly one value of y assigned to each value of x, thus making possible de nitions of functions f , and enabling us to write y f x In which cases must branches be de ned (a) From the graph of y cos x construct the graph obtained by interchanging the variables, and from which cos 1 x will result by choosing an appropriate branch. Indicate possible choices of a principal value of cos 1 x. Using this choice, nd cos 1 1=2 cos 1 1=2 . Does the value of this depend on the choice Explain. Work parts (a) and (b) of Problem 40 for (a) y sec 1 x, (b) y cot 1 x.

100 80 60 40 20 2 4 6 8 10

ListLinePlot[{list1, list2, list3}, PlotMarkers Automatic, PlotLegend {"Primes", "Fibonacci", "Squares"}, LegendPosition {1,0}]

Broadcast to resolve names. Uses a mixture of directed and broadcast UDP and TCP for resolving name. All network nodes must listen for broadcasts. Point-to-point only node. Uses directed UDP and TCP connections. Relies on access to name server to resolve names. Mixed node. Tries broadcast first and then point-to-point with name server if no response to broadcast. Hybrid node. Tries point-to-point first and then falls back to broadcast if the name server cannot be contacted. Same as an H-NODE but will also use the

months = {"Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"}; salesdata = {13.2, 15.7, 17.4, 12.6, 19.7, 22.6, 20.2, 18.3, 16.2, 15.0, 12.1, 8.6}; BarChart[salesdata, ChartLabels months]

3.41. 3.42.

m[[i,i]]

12.21 Construct a 9 9 block diagonal matrix with a 2 2 block of 2s, a 3 3 block of 3s and a 4 4 block of 4s. (A block diagonal matrix is a square partitioned matrix whose diagonal matrices are square and all others are zero matrices.)

m2 = Table[2, {2}, {2}]; m3 = Table[3, {3}, {3}];

Server Message Block (SMB)

Given the graph for y f x , show how to obtain the graph for y f ax b , where a and b are given constants. Illustrate the procedure by obtaining the graphs of (a) y cos 3x; b y sin 5x =3 ; c y tan =6 2x . Construct graphs for (a) y e jxj , (b) y ln jxj, (c) y e jxj sin x.

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