Continuity
If f(x) = {(x² - 4)/(x - 2) for x ≠ 2; k for x = 2} is continuous at x = 2, then k equals
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Solution
4
- Continuity Requirement: For f(x) to be continuous at x=2, we must have limx→2f(x)=f(2).
- Calculate Limit: For x=2, f(x)=x−2x2−4=x+2.
- limx→2(x+2)=4.
- Assign Value: From the piecewise definition, f(2)=k.
- Result: Equating the two, we get 4=k.
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About This Question
- Subject
- mathematics
- Chapter
- limit, continuity and differentiability
- Topic
- continuity
- Difficulty
- Medium
- Year
- 2025
Solution
Correct Answer:
4
- Continuity Requirement: For f(x) to be continuous at x=2, we must have limx→2f(x)=f(2).
- Calculate Limit: For x=2, f(x)=x−2x2−4=x+2.
- limx→2(x+2)=4.
- Assign Value: From the piecewise definition, f(2)=k.
- Result: Equating the two, we get 4=k.
This medium difficulty mathematics question is from the chapter limit, continuity and differentiability, covering the topic of continuity. It appeared in the 2025 exam.
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