Practice question · Sort into groups
For each described point, sort by whether the two-sided limit exists there.
Groups: Limit exists · No limit
- A jump from 4 on the left to 9 on the right
- A point where the plotted value sits far above the surrounding curve
- A vertical asymptote
- A removable hole in an otherwise smooth curve
- A sharp corner in an unbroken curve
Hints
- Ask only what the two sides approach; ignore entirely what is plotted at the point.
- A corner is a break in the slope, not a break in the values.
Show the answer
Limit exists: A removable hole in an otherwise smooth curve, A sharp corner in an unbroken curve, A point where the plotted value sits far above the surrounding curve
No limit: A jump from 4 on the left to 9 on the right, A vertical asymptote
Why
Holes, corners and misplaced single values all leave the two-sided approach intact, so the limit exists. Only a jump or an asymptote makes the two sides disagree. A corner is the instructive case: continuous, limit fine, yet it will fail differentiability in the next lesson.
Practise Limits and Continuity
The app has 6 more questions on this lesson, and keeps your place in the course. Computer Science I is free to start.
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