= Solution
{c}
Use the <Taylor expansion> $\sqrt{1-x}=1-x/2-x^2/8+O(x^3)$. Expanding the rational form gives
$$
\frac{a_0+a_1x}{1+b_1x}
=a_0+(a_1-a_0b_1)x+(a_0b_1^2-a_1b_1)x^2+O(x^3).
$$
Matching through degree two yields $a_0=1$, $a_1-b_1=-1/2$, and $b_1^2-a_1b_1=-1/8$. The last equation becomes $b_1/2=-1/8$, so
$$
\boxed{a_0=1,\qquad a_1=-\frac34,\qquad b_1=-\frac14,
\quad r(x)=\frac{1-3x/4}{1-x/4}.}
$$
This is the $[1/1]$ Padé approximant about zero. Its pole is at four, outside the <interpolation> interval; its order of matching is local and does not assert uniform minimax optimality.
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