Explain why this function is discontinuous

[dranseth]

Homework Statement

Using the test for continuity at a point, explain why each function is discontinuous at the given x-value. Classify each discontinuity.

the question is a piecewise function.

i(x)={(x^2+5x+4)/(x^3+1), x=/= -1
{2, x=-1

this is all one piece wise function.

The Attempt at a Solution

I first can say that the function exists and the limit exists just by glance. At x=-1 for the first piece, it is indeterminent. So I factor the first piece and end up with:

lim (x+4)/(x^2+x+1)
x->-1

subbing in a negative one I get 3.

but the back of the book says:

lim i(x) =2
x->-1

I'm not sure how.

 

[rock.freak667]

you should get x^2-x+1 and not x^2+x+1. But I get 1 instead of 2 still...

 

[dranseth]

nvm, the book must be wrong..

 

[Dick]

Well, for one thing you factored the denominator wrong. Are you sure the back of the book doesn't say lim(i(x))=1 as x->-1?

 

[MasterTinker]

I think the book's wrong seeing as it wants you to show why the function is not continuous, when its answer would actually show that it is continuous at x=1... I think rock freak is right on this one.