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The Maxima on-line user's manual

Algebra Calculator

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Third

Function: third (<expr>) Returns the 3rd item of expression or list <expr>. See first for more details.

load(draw);
msign(x) := if sign(x)=pos then 1 else -1 ;
nround(x,n) := float(10^-n*floor(10^n*x)) ;
nlimit(f,l) := block([g], g(x,n) := nround(f(nround(x,n)),n), map(g,map(first,l),map(second,l))) ;
p : makelist([2^-n,n+1],n,0,4);
p : append(map(lambda([x], [-first(x),second(x)]),p), reverse(p));
t : nlimit(lambda([x], [x,sin(x),sin(x)/x]), p);
draw2d(title="limit of sin(x)/x as x → 0",  nticks=200,  line_width=2,  explicit(if abs(x)<=5/200 then false else sin(x)/x,x,-1,1),  color=black, point_size=2, point_type=7,  points(map(lambda([x], [first(x),third(x)]), t)),  color=red, point_size=2, point_type=6, points([[0,1]]),  yrange=[0.8,1.05],  grid=true);

(%o1)                                true
(%i2) 

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