Practice question · Put in order
Order the checks that establish continuity of f at the point a.
- Check that the limit equals f(a)
- Declare f continuous at a
- Check that f(a) is defined
- Check that the limit of f(x) as x approaches a exists
Hints
- The third condition cannot even be stated until the first two have been settled.
- Two things must exist before they can be compared.
Show the answer
- Check that f(a) is defined
- Check that the limit of f(x) as x approaches a exists
- Check that the limit equals f(a)
- Declare f continuous at a
Why
The order is forced: comparing a value with a limit is meaningless unless both exist. A removable discontinuity passes the second check and fails the first or third, which is why the lesson insists all three conditions be verified rather than just the limit.
Practise Continuity
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More questions on Continuity
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