# Thread: find limit f(X) as x approaches __

1. ## find limit f(X) as x approaches __

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 get 1

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 limit does 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

2. ## Re: find limit f(X) as x approaches __

You have used the "direct substitution" method of limit evaluations. It works in this case, but not always.
Consider
$g(x) = \frac{x^2 - 4}{x + 2}$

And take the limit as x approaches -2. You'll find that you get 0/0, an indeterminate form.
In this example, you would factor to get "x - 2" (when x is not equal to 2) and then directly substitute.

But so far, you haven't done anything wrong!