To approximate $\sqrt{82}$ using the first-degree Taylor polynomial and the information that $\sqrt{81} = 9$, we will proceed as follows:

1. Function and point of expansion

The function we are approximating is: $f(x) = \sqrt{x}$ We are expanding around $x_0 = 81$, where we know: $f(81) = \sqrt{81} = 9$