f(x) = x^3 +3 x<-1

x^2 +x +1 -1<x<1

x^4 +2 x>1

1) for the function whose graph is given above, the limit f(x) as x approaches -1+ is:

x^2+x+1 touch -1 from right side first so I plug in -1 and get1

2) The limit f(x) as x approaches -1 is

since only x^3+3 and x^2+x+1 touches -1, I plugin -1 in both equation.

x^3+3 = 2

x^2+x+1 = 1

the limitdoes not exists.

can this method be applied to all problems similar to this one?

this is all assuming I don't have a graphic utility, don't know how to graph by hand, don't know of polynomial are contentious