Calculate the approximation of sqrt(82) using the information that sqrt(81)=9 and by linearizing function sqrt(x). Use first degree Taylor polynomial.

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:
\[
f(81) = \sqrt{81} = 9
\]



Learn how to approximate sqrt(82) using a first-degree Taylor polynomial expansion based on the known value of sqrt(81) = 9. This approach leverages linear approximation techniques from calculus and is suitable for advanced high school or early college students.

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