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The linear approximation is then, \[L\left( x \right) = 2 + \frac{1}{{12}}\left( {x - 8} \right) = \frac{1}{{12}}x + \frac{4}{3}\] Now, the approximations are nothing more than plugging the given values of \(x\) into

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The Linear Approximation formula of function f (x) is: f ( x) ≈ f ( x 0) + f ′ ( x 0) ( x − x 0) Where, f (x 0) is the value of f (x) at x = x 0. f' (x 0) is the derivative value of f (x) at x = x 0. We use Euler’s

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Find the linearization of the function f ( x) = 3 x 2 at a = 1 and use it to approximate f ( 0.9). Step 1: Find the point by substituting into the function

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The general equation for a linear approximation is f (x) ≈ f (x0) + f' (x0) (x-x0) where f (x0) is the value of the function at x0 and f' (x0) is the derivative at x0. This describes a

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In calculus, a linear approximation is an approximation of a general equation using a linear function. f (x) = f (a) + f’ (a) (x-a) The linear function whose graph is this tangent line, shown below, is called the linearization of the