limits (1 Viewer)

[oompaman]

Hi

When doing limits when are you allowed to apply the condition?
Also why is a cusp discontinuous

Thanks

 

[Carrotsticks]

Hi

When doing limits when are you allowed to apply the condition?
Also why is a cusp discontinuous

Thanks

What do you mean by applying the condition?

Also, cusps are continuous. However, they are not differentiable at the cusp.

 

[oompaman]

As in when can you "sub" in the limit
For example what's stopping you from subbing in to get 0

 

[Carrotsticks]

Can you provide an example?

 

[oompaman]

http://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityI_files/eq0034M.gif
http://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityI_files/eq0020M.gif

How do we know for the second one that we can plug in the limit without any manipulation
Is there some rule saying when you can and when you can't plug in the limit?

 

[Carrotsticks]

http://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityI_files/eq0034M.gif
http://tutorial.math.lamar.edu/Classes/CalcI/LimitsAtInfinityI_files/eq0020M.gif

How do we know for the second one that we can plug in the limit without any manipulation
Is there some rule saying when you can and when you can't plug in the limit?

If you chuck the limit in and you get in Indeterminate Form, then that means you have to keep manipulating it.

For the first one, if you chuck in x-> infinity immediately, you get infinity/infinity, which is an Indeterminate Form, so you gotta keep manipulating it somehow (for that question, it was dividing top and bottom by x^4).

 

[oompaman]

Then if a limit actually approaches 0 or infinity
how would you know when to stop manipulating?

 

[Carrotsticks]

Then if a limit actually approaches 0 or infinity
how would you know when to stop manipulating?

If you found the limit to be 0 or infinity, you're done. Those are valid limits.