Limits
The value of lim(x→∞) (3x² + 2x + 1)/(2x² - x + 3) is
Select the correct option:
Solution
3/2
- Dominant Term Analysis: In rational functions where x→∞, the behavior is determined by the highest powers of x.
- Divide by Highest Power: Divide numerator and denominator by x2:
- limx→∞2−1/x+3/x23+2/x+1/x2
- Evaluate Terms: As x→∞, terms like 2/x,1/x2 etc. approach zero.
- 2−0+03+0+0=23.
- General Rule: If degrees of numerator and denominator are equal, the limit is the ratio of their leading coefficients.
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About This Question
- Subject
- mathematics
- Chapter
- limit, continuity and differentiability
- Topic
- limits
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
3/2
- Dominant Term Analysis: In rational functions where x→∞, the behavior is determined by the highest powers of x.
- Divide by Highest Power: Divide numerator and denominator by x2:
- limx→∞2−1/x+3/x23+2/x+1/x2
- Evaluate Terms: As x→∞, terms like 2/x,1/x2 etc. approach zero.
- 2−0+03+0+0=23.
- General Rule: If degrees of numerator and denominator are equal, the limit is the ratio of their leading coefficients.
This medium difficulty mathematics question is from the chapter limit, continuity and differentiability, covering the topic of limits. It appeared in the 2025 exam.
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