Solution
= Solution
The <Maclaurin series> $\cos x=1-x^2/2+O(x^4)$ gives $e^{\cos x}=e\exp(-x^2/2+O(x^4))$. The first two nonzero terms are therefore
$$
\boxed{e^{\cos x}=e-\frac e2x^2+O(x^4).}
$$
= Solution
The <Maclaurin series> $\cos x=1-x^2/2+O(x^4)$ gives $e^{\cos x}=e\exp(-x^2/2+O(x^4))$. The first two nonzero terms are therefore
$$
\boxed{e^{\cos x}=e-\frac e2x^2+O(x^4).}
$$