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Use the definition of a Taylor series to find the first four nonzero terms of the series for $ f(x) $ centered at the given value of $ a. $

$$ f(x) = \cos^2 x, \quad a = 0 $$

$1-x^{2}+\frac{(2 x)^{4}}{4 ! \cdot 2}-\frac{(2 y)^{6}.}{6 ! \cdot 2}$

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