Pregunta
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The limit is 0.
Solución
To evaluate the limit:
Step 1: Identify the Degrees of the Polynomial
- Numerator: The highest power of
is , so the degree is 3. - Denominator: The highest power of
is , so the degree is 5.
Step 2: Compare the Degrees
When evaluating limits of rational functions as
approaches infinity:
- If the degree of the numerator is less than the degree of the denominator, the limit is 0.
- If the degrees are equal, the limit is the ratio of the leading coefficients.
- If the degree of the numerator is greater, the limit is either
or , depending on the leading coefficients.
Step 3: Apply to the Given Function
In this case:
- Degree of numerator
- Degree of denominator
Since
, the limit is:
Answer: 0
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Como
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Extra Insights
To find the limit, we can simplify the expression by dividing the numerator and the denominator by the highest power of
in the denominator, which is
:
This simplifies to:
As
approaches infinity, all terms containing
in the denominator approach zero. Therefore, we have:
Thus, the final result of the limit is:

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