limits-need help

[loganreedbishop]

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

 

[lev888]

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

1. Read posting guidelines.
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]

Read up on the squeeze theorem for limits.

 

[HallsofIvy]

What does "x go to" as x goes to 0? (That should be obvious!)
What does "[math]x^2[/math] go to" as x goes to 0? (Almost as obvious.)

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