?Verify the given linear approximation at \(a = 0\). Then determine the values of \(x\)

Chapter 2, Problem 7

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QUESTION:

Verify the given linear approximation at \(a = 0\). Then determine the values of \(x\) for which the linear approximation is accurate to within \(0.1\).

\(\tan ^{-1} x \approx x\)

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QUESTION:

Verify the given linear approximation at \(a = 0\). Then determine the values of \(x\) for which the linear approximation is accurate to within \(0.1\).

\(\tan ^{-1} x \approx x\)

ANSWER:

Step 1 of 3

Consider the equation is \(\tan ^{-1} x \approx x\).

Consider the expression for the linear approximation is \(L(x)=f(a)+f^{\prime}(a)(x-a)\).

Determine the linear approximation \(f(x)\) at \(x=0\) is \(L(x)=f(0)+x \cdot f(0)\)

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