Continuity can fail in three ways: a missing value violates the first test (the function is undefined); a jump violates the existence of a common two-sided limit (left and right limits differ); and a removable discontinuity occurs when the limit exists but differs from the assigned function value.
Conditions: The analysis applies to points where continuity is being tested.; A jump specifically means the left and right limits do not agree.; A removable discontinuity means the limit exists but does not equal .
Continuity can fail in three ways: a missing value violates the first test (the function is undefined); a jump violates the existence of a common two-sided limit (left and right limits differ); and a removable discontinuity occurs when the limit exists but differs from the assigned function value.
Conditions: The analysis applies to points where continuity is being tested.; A jump specifically means the left and right limits do not agree.; A removable discontinuity means the limit exists but does not equal .