>	with(plots):

Warning, the name changecoords has been redefined

>	f:=(x^4)*cos(100*Pi*x);

>	Limit(f,x=2);

>

value(%);

>	point1:=pointplot([2,16],color=blue):

>	curve1:=plot(f,x=1.9..2.1,y=-20..20,labels=[x,y],thickness=2,axes=boxed):

>	display(curve1,point1);

>	curve2:=plot(f,x=1.999..2.001,y=15.999..16.001,labels=[x,y],thickness=2,axes=boxed):

The curve is plotted below with a delta value of 0.001 and epsilon equal to 0.001 but not enough points are used in constructing the plot (the default number of points used is 50).

>	display(curve2,point1);

More points are being used in constructing the graph.

>	curve2:=plot(f,x=1.999..2.001,y=15.999..16.001,labels=[x,y],thickness=2,axes=boxed,numpoints=200):

>	display(curve2,point1);

In the graph below the delta value is 0.0001.

>	curve3:=plot(f,x=1.9999..2.0001,y=15.999..16.001,labels=[x,y],thickness=2,axes=boxed,numpoints=200):

>	display(curve3,point1);

In the graph below the delta value is 0.00001.

>	curve4:=plot(f,x=1.99999..2.00001,y=15.999..16.001,labels=[x,y],thickness=2,axes=boxed,numpoints=200):

>	display(curve4,point1);

This time delta equals 0.00002.

>	curve5:=plot(f,x=1.99998..2.00002,y=15.999..16.001,labels=[x,y],thickness=2,axes=boxed,numpoints=200):

>	display(curve5,point1);

Here we have a delta value of 0.0000206 which is just about as large as delta can be when epsilon equals 0.001.

>	curve6:=plot(f,x=1.9999794..2.0000206,y=15.999..16.001,labels=[x,y],thickness=2,axes=boxed,numpoints=200):

>	display(curve6,point1);

>