Podcast
Questions and Answers
What is the difference between a removable and non-removable discontinuity?
What is the difference between a removable and non-removable discontinuity?
- A removable discontinuity occurs when the function approaches a finite limit from both sides, while a non-removable discontinuity occurs when the function approaches different limits from both sides
- A removable discontinuity is always a vertical asymptote, while a non-removable discontinuity can be a hole or jump
- A removable discontinuity can be fixed by redefining the function at the point of discontinuity, while a non-removable discontinuity cannot (correct)
- A removable discontinuity is always a hole in the graph of the function, while a non-removable discontinuity can be a jump or infinite oscillation
Which of the following statements is true about the limit of a function?
Which of the following statements is true about the limit of a function?
- The limit of a function does not exist if the function is not continuous at that point (correct)
- The limit of a function always exists if the function is continuous at that point
- The limit of a function is always equal to infinity at a vertical asymptote
- The limit of a function and the value of the function at that point are always the same
Which of the following is true about one-sided limits?
Which of the following is true about one-sided limits?
- A one-sided limit does not exist if the function approaches different values from both sides
- A one-sided limit always equals the two-sided limit
- A one-sided limit exists if the function approaches the same value from both sides (correct)
- A one-sided limit exists if the function approaches infinity from both sides
Flashcards
Removable Discontinuity
Removable Discontinuity
A removable discontinuity can be 'fixed' by changing the function's value at the point of discontinuity. Think of it like patching a hole in a road.
Non-removable Discontinuity
Non-removable Discontinuity
A non-removable discontinuity cannot be fixed by simply changing the function's value at the point of discontinuity.
One-Sided Limit
One-Sided Limit
A one-sided limit exists if the function approaches the same value from both the left and the right sides of the point.
