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Which of the following is true?

  1. $\log(1+x) < x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for all } x>0$
  2. $\log(1+x) > x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for all } x>0$
  3. $\log(1+x) > x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for some } x>0$
  4. $\log(1+x) < x- \frac{x^2}{2} + \frac{x^3}{3} \text{ for some } x>0$
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