# Equation for linear approximation

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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## Calculus I

linear\:approximation\:f(x)=x+\frac{1}{x},\:a=-1; linear\:approximation\:\sin(\frac{\pi}{3}) linear\:approximation\:f(x)=\sqrt{x},\:a=4; linear\:approximation\:\sin(x),\:a=\frac{\pi}{6}

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## Understanding linear approximation in calculus

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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## The linear approximation

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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## Linear Approximation Formula

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