#### loganreedbishop

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

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

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1. Read posting guidelines.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).

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

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