If `f(x)=sqrt(x^2+9)` , write the value of `(lim)_(x->4)(f(x)-f(4))/(x-4)` .

Explanation

To solve the limit \( \lim_{x \to 4} \frac{f(x) - f(4)}{x - 4} \) where \( f(x) = \sqrt{x^2 + 9} \), we will follow these steps:

### Step 1: Calculate \( f(4) \)
First, we need to find \( f(4) \):
\[ f(4) = \sqrt{4^2 + 9} = \sqrt{16 + 9} = \sqrt{25} = 5 \]

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