Homework Section 3.4
Calculus I
Andy Long

#9, p. 235

f[x_]:=(3x-2)/(2x+1)
lim=Limit[f[x],x->Infinity]
Plot[{lim,f[x]},{x,0,20},PlotRange->All]

#12, p. 235

f[x_]:=(4x^3+6x^2-2)/(2x^3-4x+5)
lim=Limit[f[x],x->-Infinity]
Plot[{lim,f[x]},{x,-20,20}]

#15, p. 235

f[x_]:=(2x^2+1)^2/((x-1)^2*(x^2+x))
lim=Limit[f[x],x->Infinity]
Plot[{f[x],lim},{x,0,20},PlotRange->{{0,20},{0,6}}]

#18, p. 235

f[x_]:=Sqrt[9x^6-x]/(x^3+1)
lim=Limit[f[x],x->-Infinity]
Plot[{lim,f[x]},{x,-20,-5},PlotRange->All]

#23, p. 235

f[x_]:=(x^4-3x^2+x)/(x^3-x+2)
lim=Limit[f[x],x->Infinity] (* this does have a slant asymptote, however: *)
Plot[{x,f[x]},{x,0,10},PlotRange->All]

#46, p. 235

f[x_]:=x/Sqrt[x^2+1]
lim=Limit[f[x],x->Infinity] (* this does have a slant asymptote, however: *)
Plot[{lim,-lim,f[x]},{x,-10,10},PlotRange->All]