Using bounds, the correct statement is given by:
The order is odd and the leading coefficient is negative.
As x approaches infinity it is detected by its limit. On the left side, it is given by:
- Rim x -> - ∞ f(x)
- On the right-hand side, it is given by
- Rim x -> ∞ f(x)
- Since x tends to infinity, this is the limit, so we only consider the highest order term and its predecessors.
- So the described behavior is i. H. lim→→ = ∞, lim⭑→∞ =1∞ if:
- The order is odd and the leading coefficient is negative.
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