Tables and Graphs

Here is an expression f.

> f:=x^2-4*x+3;

[Maple Math]

Make a table of values for f with x from -1 to 5 in steps of 0.5. (The next command loads the package math191 which contains many custom Maple commands that will be used including the one to make a table of values.)

> with(math191):

> valutable(f,x=-1..5,'step'=0.5); 

 x             funct(x)   
----------------------------
-1.           8.            
-.5000000000  5.250000000   
0             3.            
.500000000    1.250000000   
1.000000000   0             
1.500000000   -.750000000   
2.000000000   -1.000000000  
2.500000000   -.750000000   
3.000000000   0             
3.500000000   1.25000000    
4.000000000   3.            
4.500000000   5.25000000    
5.000000000   8.00000000    
.......Remember that the user did not have to type in the Maple commands or custom Maple commands which are in red.......

Now plot the points in this table.

> plotvalutable(f,x=-1..5,'step'=0.5);

[Maple Plot]

Make a graph of f using graph paper.

> gpplot(f,x=-1..5,y=-1..8,color=blue);

[Maple Plot]

Make a table to see what happens to an expression for values of x near a vertical asymptote.

> g:=(2*x-6)/(x-1);

[Maple Math]

> limtab(g,x=1,right); 

     x            func(x) 
----------------------------
 1.100000000     -38.00000000  
 1.010000000     -398.0000000  
 1.001000000     -3998.000000  
 1.000100000     -39998.00000  
 1.000010000     -399998.0000  
 1.000001000     -3999998.000  
 1.000000100     -39999998.00

> limtab(g,x=1,left); 

     x            func(x) 
----------------------------
 .9000000000      42.00000000  
 .9900000000      402.0000000  
 .9990000000      4002.000000  
 .9999000000      40002.00000  
 .9999900000      400002.0000  
 .9999990000      4000002.000  
 .9999999000      40000002.00

> plot(g,x=-1..3,y=-100..100);

[Maple Plot]

Make a table to see what happens to g for large values of x.

> limtab(g,x=infinity); 

     x            func(x) 
----------------------------
 .1000000000        6.444444444  
 10.00000000        1.555555556  
 1000.000000        1.995995996  
 100000.0000        1.999960000  
 10000000.00        1.999999600  
 1000000000.        1.999999996  
 0.1000000000E12    2.000000000

Has it really gotten to three? Change to 12 digits to see.

> Digits:=12;

[Maple Math]

> limtab(g,x=infinity); 

     x              func(x)   
--------------------------------
 .100000000000      6.44444444444  
 10.0000000000      1.55555555556  
 1000.00000000      1.99599599600  
 100000.000000      1.99995999960  
 10000000.0000      1.99999960000  
 1000000000.00      1.99999999600  
 100000000000.      1.99999999996

> Digits:=10;

[Maple Math]

.......With MenuMaple the user selects an action button for a Maple command or custom Maple command and enters required information after being prompted.........