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?Verify the given linear approximation at \(a = 0\). Then determine the values of \(x\)
Chapter 2, Problem 7(choose chapter or problem)
QUESTION:
Verify the given linear approximation at \(a = 0\). Then determine the values of \(x\) for which the linear approximation is accurate to within \(0.1\).
\(\tan ^{-1} x \approx x\)
Questions & Answers
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 \(L(x)=f(0)+x \cdot f(0)\)