Continuity
A function f(x) is continuous at x = a if
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Solution
lim(x→a) f(x) = f(a)
By definition, for a function f to be continuous at a point x=a, three specific criteria must be met:
- Defined at point: f(a) must exist (no holes or asymptotes).
- Limit exists: limx→af(x) must exist (Left-hand limit = Right-hand limit).
- Consistency: The limit as x approaches a must exactly equal the function's value at a, i.e., limx→af(x)=f(a). This ensures there is no 'jump' at a.
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About This Question
- Subject
- mathematics
- Chapter
- limit, continuity and differentiability
- Topic
- continuity
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
lim(x→a) f(x) = f(a)
By definition, for a function f to be continuous at a point x=a, three specific criteria must be met:
- Defined at point: f(a) must exist (no holes or asymptotes).
- Limit exists: limx→af(x) must exist (Left-hand limit = Right-hand limit).
- Consistency: The limit as x approaches a must exactly equal the function's value at a, i.e., limx→af(x)=f(a). This ensures there is no 'jump' at a.
This easy 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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