Explain why the rules for limits at infinity should be true. The behavior of f(x
ID: 2857366 • Letter: E
Question
Explain why the rules for limits at infinity should be true.
The behavior of f(x) as x approaches infinity is determined by the degrees of p(x) and q(x). If the degree of q(x) is greater than the degree of p(x), q(x) will approach infinity
1) _________
than p(x), and thus f(x) will approach
2. ______
as x approaches infinity. If the degree of q(x) is less than the degree of p(x), q(x) will approach infinity
3. ________
than p(x), and thus f(x) will approach
4. _________
as x approaches infinity. If the degree of q(x) is the same as the degree of p(x), q(x) will approach infinity at the same rate as p(x), and thus f(x) will approach
5. _________
as x approaches infinity.
Choose 1 answer
1. slower / faster
2. a constant/ zero/ infinity
3. slower / faster
4. zero / infinity / a constant
5. a constant/ zero / infinity
Explanation / Answer
f(x)= p(x)/q(x)
If the degree of q(x) is greater than the degree of p(x), q(x) will approach infinity
1) faster
than p(x), and thus f(x) will approach
2. zero
as x approaches infinity. If the degree of q(x) is less than the degree of p(x), q(x) will approach infinity
3. slower
than p(x), and thus f(x) will approach
4. infinity.
as x approaches infinity. If the degree of q(x) is the same as the degree of p(x), q(x) will approach infinity at the same rate as p(x), and thus f(x) will approach
5. a constant
as x approaches infinity.
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