Linear Approximation (How To w/ Step-by-Step Examples!)

Find the linear approximation of \(f(x)=(1+x)^n\) at \(x=0\). Use this approximation to estimate \((1.01)^3.\) Solution. The linear approximation at \(x=0\) is given by
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Differentials in Linear Approximation

f ( 1) = 3 ( 1) 2 = 3 ( 1, 3) Step 2: Find the derivative f' (x). f ′ ( x) = 6 x. Step 3: Substitute into the derivative to find f' (a). f ′ ( 1) = 6 ( 1) = 6 m = 6. Step 4: Write the equation of the tangent line using the point and slope found in

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