Thread: Limit does not exist

Hey,

I have a question where x is approaching zero from the left side but when I try substitution it works out to number/0

absolute value x / [[x+1]]

(double bracket on denominator is supposed to be greatest possible integer less than or equal)

When I approach the bottom part from the left I get a number less than 1 meaning the greatest possible integer is 0

This means that the limit does not exist right?

Where as if I didn't specify whether x approaches 0 from the left or the right I would not say the limit does not exist and instead look at the limit from the left and right side right?



Uhh just to clarify my question uhh... I'm trying to ask under what circumstances does the limit not exist, is it only if the left and right do not equal each other or if the limit of the left side (or right) end up equalling a number/0

thanks

And sorry for long post Next time it will be shorter (hopefully)

Originally Posted by Mudd_101

I'm trying to ask under what circumstances does the limit not exist, is it only if the left and right do not equal each other or if the limit of the left side (or right) end up equalling a number/0

For the limit to exist, the limit from the left and the limit from the right must both exist and they must be equal.

Originally Posted by Mudd_101

Hey,

I have a question where x is approaching zero from the left side but when I try substitution it works out to number/0

absolute value x / [[x+1]]

(double bracket on denominator is supposed to be greatest possible integer less than or equal)

When I approach the bottom part from the left I get a number less than 1 meaning the greatest possible integer is 0

No. The greatest integer less than or equal to -.2, say, is -1. For x between -1 and 0, this function is x/-1= -x and its limit is 0. It is the limit from the right that does not exist: if x is between 0 and 1 then the denominator is 0 so the function does not exist for any x getween 0 and 1.

[snip]This means that the limit does not exist right?

Where as if I didn't specify whether x approaches 0 from the left or the right I would not say the limit does not exist and instead look at the limit from the left and right side right?



Uhh just to clarify my question uhh... I'm trying to ask under what circumstances does the limit not exist, is it only if the left and right do not equal each other or if the limit of the left side (or right) end up equalling a number/0

thanks

And sorry for long post Next time it will be shorter (hopefully)