What does 'infinite discontinuity' mean?Context: "In the function 1/[(x+3)(x-2)], there is are infinite discontinuities at x=2 and at x=3"
Infinite discontinuity means the function goes to infinity at that point.
The two points for your function are x=-3 and x=2.
We can see which direction the discontinuity goes by making a sign chart.
x<-3 1/((x+3)(x-2)) is 1/((-)(-))=+
-3<x<2 1/((x+3)(x-2)) is 1/((+)(-))=-
x>2 1/((x+3)(x-2)) is 1/((+)(+))=+
So on the left of -3 the function goes to positive infinity,
On the right of -3 the function comes from negative infinity
On the left of 2 the function goes to negative infinity
On the right of 2 the function comes from positive infinity.
If you graph the function you might see the idea better.