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When does the limit of a function at a point exist?
ABoth sides approach one value
BThe function is defined there
CThe graph has no sharp corner
DThe function is always rising
Answer & Solution
Correct answer: A. Both sides approach one value
1. A limit asks what value a function heads towards as the input creeps up on a chosen point.
2. The input can creep up from the left or from the right, and the two need not agree.
3. The limit exists only when the function heads for the same value from both sides.
4. If the two sides head for different values, the limit at that point does not exist.
5. A function can have a limit at a point where it is not even defined, so being defined there is not the test.
_Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 6: Differential calculus_
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