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Which of the following functions would have only odd powers of $x$ in its Taylor series expansion about the point $x=0?$ 

  1. $\sin \left(x^{3}\right)$
  2. $\sin \left(x^{2}\right)$
  3. $\cos \left(x^{3}\right)$
  4. $\cos \left(x^{2}\right)$
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