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

Explanation

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

### Step 1: Define the function
Let \( y = f(x) = \sqrt{x} \).

### Step 2: Choose a point close to 49.5
We choose \( x = 49 \) because it is a perfect square and close to 49.5. Thus, we have:
\[
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