How do I find the limit as #x# approaches negative infinity of a polynomial?
2 Answers
If the polynomial
Explanation:
We can use the following fact about polynomials:
If
This fact is really saying that when we take a limit at infinity for a polynomial, all we have to do is look at the term with the largest power and ask what that term is doing in the limit.
If
If
I usually do this informally.
Explanation:
I ask myself what kinds of numbers do I get if I put in more and more negative numbers for
Examples:
Example 1
For very very big numbers, the only term that matters is the largest power term:
Example 2
For very very big numbers, the only term that matters is the largest power term:
Example 3 (last)
For very very big numbers, the only term that matters is the largest power term: