Find the linear approximation of f(x) = (1 + x)4 at x = 0 without using the result from the preceding example. Differentials We have seen that linear approximations can be used to estimate

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Example 1 Determine the linear approximation for f (x) = 3√x f ( x) = x 3 at x = 8 x = 8. Use the linear approximation to approximate the value of 3√8.05 8.05 3 and 3√25 25 3 . Linear approximations do a very good job of

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Find the linear approximation of f ( x) = ( 1 + x) n at x = 0. Use this approximation to estimate ( 1.01) 3. Find the linear approximation of f ( x) = ( 1 + x) 4 at x = 0 without using the result from

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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A linear approximation is a linear function that approximates something. A typical formula for a good linear approximation uses the value of the function at a point along with

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