Limits
The value of lim(x→0) (sin x)/x is
Select the correct option:
Solution
1
- Indeterminate Form: As x→0, sinx→0, resulting in 0/0.
- Standard Limit: This is a fundamental trigonometric limit derived using Squeeze Theorem or Taylor series expansion.
- sinx=x−3!x3+5!x5−…
- xsinx=1−3!x2+5!x4−…
- Result: As x→0, all terms with x vanish, leaving limx→0xsinx=1.
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About This Question
- Subject
- mathematics
- Chapter
- limit, continuity and differentiability
- Topic
- limits
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
1
- Indeterminate Form: As x→0, sinx→0, resulting in 0/0.
- Standard Limit: This is a fundamental trigonometric limit derived using Squeeze Theorem or Taylor series expansion.
- sinx=x−3!x3+5!x5−…
- xsinx=1−3!x2+5!x4−…
- Result: As x→0, all terms with x vanish, leaving limx→0xsinx=1.
This easy 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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