Practice question · Multiple choice
A function can have a limit of 5 at while , or while does not exist at all. What does that show about what a limit measures?
Hints
- Look at which -values the definition actually uses.
- Ask what the difference quotient equals exactly at .
Show the answer
C. That it describes what the function APPROACHES, not its value
Why
Deliberately ignoring the point is the whole design. Without it the derivative could not be defined, because the difference quotient is undefined precisely where the derivative is being taken.
Practise Limits and continuity
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