Is the Limit of the Sum Always the Sum of the Limits?

[Jacobpm64]

I have a few conceptual questions on limits that i need help with..

1. A student in your class says, "The limit of the sum of two functions is the sum of the limits of the functions." When is the statement not correct?

I'm not sure. I thought it was always correct because doesn't one of the theorems actually say that the limit of the sum of two functions is the sum of the limits of the functions. Is there an exception I'm missing?

2. Express the limit of (x-1)^3 as x approaches 3 in two different ways.

hmm.. I'm not sure what they want right here

 

[matt grime]

1. yes you are missing something. try rereading your notes.

2. no, i don't know either. the limit is 8. perhaps they also want you to say it is 16/2, who knows.

 

[Jacobpm64]

i think for number 1.. lim f + g = lim f + lim g ... if lim f and lim g both exist.

I still don't know about #2 though

 

[dav2008]

For 2 they probably want the limit from the left, and from the right.

 

[HallsofIvy]

Well, one way to express "the limit of (x-1)^3 as x approaches 3" is "8"!