read "Anim.mpl":
with(plots):
h:=x->1+floor(1-abs(x)/2):
#read "khtools.m":
with(student):
Lh:=[seq(middlebox(h(x),x=-1..1,n),n=5..49)]:
display(Lh,insequence=true);
dh:=0.99*abs(x)+(floor(1-abs(x)/2))/(2*n):
Delh:=[seq(evalf(dh),n=1..25)]:
DELh:=[seq(unapply(Delh[i],x),i=1..25)]:
display(
[
seq(khbox(h,-1,1,DELh[i]),i=1..25)
],insequence=true);
f3:=x->1+(6-2*abs(x))*(floor(1+x)-ceil(x)):
Lf3:=[seq(leftbox(f3(x),x=-3..3,4*n),n=3..24)]:
display(Lf3,insequence=true);
df3:=0.99*abs(x-round(x))+(floor(1+x)-ceil(x))*(f3(x)+n)^(-1):
Delf3:=[seq(evalf(df3),n=0..25)]:
DELf3:=[seq(unapply(Delf3[i],x),i=1..25)]:
display(
[
seq(khbox(f3,-3,3,DELf3[i]),i=1..25)
],insequence=true);
f2:=x->1-x^4;
L2:=[seq(middlebox(f2(x),x=-1..1,n),n=4..50)]:
display(L2,insequence=true);
d2:=min( (0.85/n)^(1/4),0.85/( n*( abs(x)+(0.75/n)^(1/4) )^3 ) ):
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
Del2:=[seq(evalf(d2),n=1..25)]:
DEL2:=[seq(unapply(Del2[i],x),i=1..25)]:
display(
[
seq(khbox(f2,-1,1,DEL2[i]),i=1..25)
],insequence=true);
s:=x->sin(Pi/x):
s1:=diff(s(x),x):
s2:=diff(s(x),x,x):
Ls:=[seq(middlebox(s(x),x=0.25..2,n),n=4..25)]:
display(Ls,insequence=true);
ds:=max(0.015,min(2/n,1/(n*abs(s1)+0.6*abs(s2)) )):
Dels:=[seq(evalf(ds),n=1..25)]:
DELs:=[seq(unapply(Dels[i],x),i=1..25)]:
display(
[
seq(khbox(s,0.25,2,DELs[i]),i=1..25)
],insequence=true);
khbox(s,0.25,2,DELs[25]):
f1:=proc(x)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
local f:
if x=0 then f:=0;
else f:=-ln(abs(x));
end if:
end:
d1:=floor(1-abs(x)/2)/(3*n)+2*abs(x)*(exp(1/n)-1)/(exp(1/n)+1):
Del1:=[seq(evalf(d1),n=1..10)]:
DEL1:=[seq(unapply(Del1[i],x),i=1..10)]:
display(
[
seq(khbox(f1,-1,1,DEL1[i],y=0..4),i=2..10)
],insequence=true);