Using differentials, find the approximate value of `sqrt(49. 5)`

Explanation

To find the approximate value of \( \sqrt{49.5} \) using differentials, we can follow these steps:

### Step 1: Identify the function and point of approximation
Let \( f(x) = \sqrt{x} \). We will use \( x = 49 \) because it is close to \( 49.5 \) and we know \( \sqrt{49} = 7 \).

### Step 2: Calculate the differential
The differential \( df \) can be expressed as:
\[
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