Formal Definition of Limit
Let be a function defined on an interval around , although perhaps not at itself. The limit of as approaches is if gets really close to whenever gets really close to .
To say this formally, if for every there exists for which whenever .
The construction below helps make this more intuitive. Pick to set a vertical range for around . Then set small enough that the pink brick fits inside the blue strip.
Let be a function defined on an interval around , although perhaps not at itself. The limit of as approaches is if gets really close to whenever gets really close to .
To say this formally, if for every there exists for which whenever .
The construction below helps make this more intuitive. Pick to set a vertical range for around . Then set small enough that the pink brick fits inside the blue strip.
Let be a function defined on an interval around , although perhaps not at itself. The limit of as approaches is if gets really close to whenever gets really close to .
To say this formally, if for every there exists for which whenever .
The construction below helps make this more intuitive. Pick to set a vertical range for around . Then set small enough that the pink brick fits inside the blue strip.