Basic Examples (9)
Basic Examples
(9)
Compute the asymptotes of a decaying exponential:
In[4]:=
Out[4]=
Horizontal{{y8,x∞}}
In[5]:=
Plot[{Exp[-x]+8,8},{x,0,3},PlotRange{7.5,9},PlotStyle->{Lighter[Blue,0.5],{{Red,Dashed,Thick}}}]
Out[5]=
———
Compute the asymptotes of a hyperbola:
In[6]:=
Out[6]=
Horizontal{{y0,x±∞}},Vertical{{y±∞,x0}}
In[7]:=
Plot[{1/x,0},{x,-3.5,3.5},PlotRange{-3.5,3.5},PlotStyle->{Lighter[Blue,0.5],{{Red,Dashed,Thick}}},ExclusionsStyle{{Red,Dashed,Thick},{PointSize0.0}}]
Out[7]=
———
Compute the asymptotes of a rational function:
In[8]:=
Out[8]=
Vertical{{y±∞,x-1}},Oblique{{yx,x±∞}}
In[9]:=
Plot[{(x^2+x+1)/(x+1),x},{x,-4,3},PlotStyle->{Lighter[Blue,0.5],{{Red,Dashed,Thick}}},ExclusionsStyle{{Red,Dashed,Thick},{PointSize0.0}}]
Out[9]=
———
Compute only the oblique asymptotes of the previous function:
In[10]:=
Out[10]=
{{yx,x±∞}}
———
Compute the asymptotes of a periodic function:
In[11]:=
Out[11]=
Verticaly±∞,x-+2π,y±∞,x+2π
π
2
1
π
2
1
In[12]:=
Plot[Tan[x],{x,-5,5},ExclusionsStyle{{Red,Dashed,Thick},{PointSize0.0}}]
Out[12]=
———
Compute the asymptotes of an algebraic function:
In[79]:=
Out[79]=
Obliquey(-1-2x),x-∞,y(1+2x),x∞
1
2
1
2
In[80]:=
Plot[{(x^2+x+5)^(1/2),-1/2-x,1/2+x},{x,-6,5},PlotRange{-1,6},PlotStyle->{Lighter[Blue,0.5],{{Red,Dashed,Thick}},{{Red,Dashed,Thick}}}]
Out[80]=
———
Compute a list of all asymptotes of the previous function:
In[81]:=
Out[81]=
y(-1-2x),x-∞,y(1+2x),x∞
1
2
1
2
———
Compute the asymptotes of another algebraic function:
In[117]:=
Out[117]=
Oblique{{yx,x∞}}
In[118]:=
Plot[{(x^3+1)^(1/3),x},{x,-1.5,2},PlotStyle->{Lighter[Blue,0.5],{{Red,Dashed,Thick}},{{Red,Dashed,Thick}}}]
Out[118]=
———
Compute the asymptotes of a transcendental function:
In[84]:=
Out[84]=
Obliquey(-π+4x),x-∞,y(π+4x),x∞
1
2
1
2
In[85]:=
Plot[{ArcTan[x]+2x,2x-Pi/2,2x+Pi/2},{x,-1.5,2},PlotStyle->{Lighter[Blue,0.5],{{Red,Dashed,Thick}},{{Red,Dashed,Thick}}}]
Out[85]=