Practice question · Select all that apply
Select every condition that must hold for f to be continuous at the point a.
Hints
- The lesson lists exactly three requirements, and all three must hold together.
- Two of the options describe particular functions rather than a general requirement.
Show the answer
- B. f(a) is defined
- C. the limit of f(x) as x approaches a exists
- D. the limit of f(x) as x approaches a equals f(a)
Why
Continuity needs the value to exist, the limit to exist, and the two to agree. Polynomials happen to be continuous everywhere, but being a polynomial is not a requirement, and f(a) = 0 has nothing to do with it.
Practise Limits and Continuity
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