Small-argument expansion of the hyperbolic tangent
= Small-argument expansion of the hyperbolic tangent
{title2=$\tanh x=x+O(x^3)$}
The <taylor series> at zero begins
$$
\tanh x=x-\frac{x^3}{3}+O(x^5),
$$
so $\tanh x\sim x$ as $x\to0$.
= Small-argument expansion of the hyperbolic tangent
{title2=$\tanh x=x+O(x^3)$}
The <taylor series> at zero begins
$$
\tanh x=x-\frac{x^3}{3}+O(x^5),
$$
so $\tanh x\sim x$ as $x\to0$.