alleryf(x) is discontinuous at x = a if which condition fails?
AAny of the above failing makes f discontinuous
Bf(a) defined
CLimit at x = a exists
Df(a) equals the limit at x = a
Answer & Solution
Correct answer: A. Any of the above failing makes f discontinuous
Continuity requires all 3 conditions.
Failure of any one creates discontinuity.
**Different types:** removable (limit exists but f(a) wrong), jump (one-sided limits differ), infinite (limit is ±∞), oscillating (no limit).
Keep practising Unit 1B1: Limit Concepts and Graphical Limits
Browse all Unit 1B1: Limit Concepts and Graphical Limits questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
Which of the following is a rational number?Which statement is true for a polynomial of degree $n$?If $(d,m,n)$ are direction cosines of a line, which relation must hold?If $A$ is a square matrix with $|A| = 3$ and order $n = 3$, then $|\operatorname{adj}(A)|$For a non-singular $n \times n$ matrix $A$, the relation between $\det(\operatorname{adj} A square matrix $A$ is **invertible** if and only if:If $A$ and $B$ are matrices for which $AB$ is defined, then $(AB)'$ equals:The diagonal entries of any skew-symmetric matrix are: