# limits-need help

#### loganreedbishop

##### New member
If x^3 <= f(x) <= x for x in [-1,1], find limit as x approaches 0 of f(x) if it exists.

#### lev888

##### Elite Member
If x^3 <= f(x) <= x for x in [-1,1], find limit as x approaches 0 of f(x) if it exists.
2. Graph the functions. What do you think is the limit?
3. Prove that the limit is what you think it is. I would use proof by contradiction (any other limit would contradict the definition of limit).

#### Steven G

##### Elite Member
Read up on the squeeze theorem for limits.

#### HallsofIvy

##### Elite Member
What does "x go to" as x goes to 0? (That should be obvious!)
What does "$x^2$ go to" as x goes to 0? (Almost as obvious.)

And f(x) is "trapped" between them.