L'Hopital's Rule

examples

>	with(plots):

Warning, the name changecoords has been redefined

>	f:=sin(4*x)/(2*x);

>	Limit(f,x=0);

>

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

>	g:=sqrt(4-x^2)/(x-2);

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

>

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

>	h:=ln(x^4)/x^3;

>	Limit(h,x=infinity);

>

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>	plot(h,x=1..20,thickness=2);

>	f2:=(x^3)*cot(x);

>	Limit(f2,x=0,right);

>

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>	plot(f2,x=-2..2,thickness=2);

>	g2:=(1+1/x)^x;

>	Limit(g2,x=infinity);

>

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>	pic1:=plot(exp(1),x=0..100,thickness=2,color=blue):

>	pic2:=plot(g2,x=0..100,thickness=2):

>	display(pic1,pic2);

>	h2:=(sin(x))^x;

>	plot(h2,x=0..2,thickness=2);

>	eval(h2,x=0.0001);

>	eval(h2,x=0.0000001);

>	eval(h2,x=0.0000000001);

>	eval(h2,x=0.0000000000001);

>	Limit(h2,x=0,right);

>

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>