Limits 

Some Computations 

>	with(plots):

 

Warning, the name changecoords has been redefined
 

If you use a small "l" in the "limit" command then Maple computes the limit. 

>	limit(x*sin(1/x),x=0);

 

>	limit(sin(x)/x,x=0);

 

>	limit((1-cos(x))/x,x=0);

 

>	limit((sqrt(x+1)-2)/(x-3),x=3);

 

If you use a capital "L" in the "Limit" command then Maple displays the command. 

>	Limit((1/(x+4)-1/4)/x,x=0);

 

You can then use the "value" command to evaluate the output of the previous command which is represented by the "%". 

>

value(%);

 

>	limit(sin(7*t)/(3*t),t=0);

 

>	Limit(tan(x)/x,x=0);

 

>

value(%);

 

>	Limit(tan(x)^2/x,x=0);

 

>

value(%);

 

Piecewise defined functions are looked at below. 

>	f:=x->piecewise(x<2,x+5,x^2+2);

 

>	plot(f(x),x=0..4,thickness=2);

 

>	plot(f(x),x=0..4,thickness=2,discont=true);

 

>	Limit(f(x),x=2);

 

>

value(%);

 

>	limit(f(x),x=2,left);

 

>	limit(f(x),x=2,right);

 

>	g:=x->piecewise(x<-2,-3,x<=1,x-2,x^2-2);

 

>	plot(g(x),x=-4..3,thickness=2,discont=true);

 

>	Limit(g(x),x=-2);

 

>

value(%);

 

>	Limit(g(x),x=1);

 

>

value(%);

 

>	limit(g(x),x=-2,left);

 

>	limit(g(x),x=-2,right);