Solution
= Solution
Use $\sin x=x-x^3/6+O(x^5)$ inside the <exponential series>:
$$
e^{\sin x}=1+\left(x-\frac{x^3}{6}\right)+\frac{x^2}{2}
+\frac{x^3}{6}+O(x^4).
$$
The two cubic contributions cancel, leaving
$$
\boxed{e^{\sin x}=1+x+\frac{x^2}{2}+O(x^4).}
$$
Thus the <coefficient> of $x^3$ is zero, even though the <function> itself is not an <even function>.