### Homework 8 1) **Find the linear approximation** \( L(x) \) to \( y = f(x) \) near \( x = a \) for the function: \[ f(x) = \frac{1}{x}, \quad a = 4 \] \[ L(x) = \] --- *Note: Continue filling in the expression for \( L(x) \) using the formula for linear approximation:* \[ L(x) = f(a) + f'(a)(x - a) \] *Determine \( f'(x) \), evaluate at \( x = a \), and substitute into the formula.*

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