Practice question · True or false
Continuity at a point requires three separate conditions, and the limit existing is only one of them.
Hints
- What else must hold?
- The value must exist, and match.
Show the answer
True
Why
True. must be defined, must exist, and the two must be equal. A removable discontinuity satisfies the second and fails the third; a function undefined at fails the first. Each condition rules out a different failure, which is why the definition lists all three.
Practise Continuity
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More questions on Continuity
- Sort each function by whether it is continuous at every real number.
- Order the checks that establish continuity of f at the point a.
- The function |x| is continuous everywhere and has no derivative at 0. What does that pair of facts establish…
- f is continuous on the closed interval from 0 to 4. Select every statement that MUST be true.