Exams › GATE › Engineering Mathematics

If a function is continuous at a point,

1. the limit of the function may not exist at the point
2. the function must be derivable at the point
3. the limit of the function at the point tends to infinity
4. the limit must exist at the point and its value should be the same as the value of the function at that point

Correct answer: the limit must exist at the point and its value should be the same as the value of the function at that point

Solution

A function is continuous at a point if the limit exists there and equals the function value at that point. Continuity does not imply differentiability. Therefore the correct statement is the one matching the definition of continuity.

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