3.5 Limits at Infinity First lets look at some math that will be important for what we are doing We have discussed dividing by 0 as being UNDEFINED. What does that mean? 1 4 −6
What kind of limits did we get when we had , , ? 0 0 0
What happens when we divide by really SMALL numbers? 2
What is = .1
2
= .01
2
= .001
2
= .0001
2
= 0
Now what happens when we divide numbers by really BIG numbers? This will be important for Limits at infinity 2
= 10
2
= 100
2
= 1000
2
= 10,000
2
= ∞
3x 2
Graph f (x) = 2
x +1
As we go way out to the right of the graph, where does it look like the graph is headed (y value)? What about way out to the left? What is this called? How can we find that algebraically? Find lim
x→∞
2x − 1
x +1
2x + 5
x→∞ 3x 2 + 1
2x 3 + 5
lim 2
x→∞ 3x + 1
lim
lim
x→∞
3x − 2
2x 2 + 1