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?Find the linear approximation of the function\(f(x)=\sqrt{1-x}\) at \(a = 0\) and use
Chapter 2, Problem 5(choose chapter or problem)
QUESTION:
Find the linear approximation of the function \(f(x)=\sqrt{1-x}\) at \(a = 0\) and use it to approximate the numbers \(\sqrt{0.9}\) and \(\sqrt{0.99}\). Illustrate by graphing \(f\) and the tangent line.
Questions & Answers
QUESTION:
Find the linear approximation of the function \(f(x)=\sqrt{1-x}\) at \(a = 0\) and use it to approximate the numbers \(\sqrt{0.9}\) and \(\sqrt{0.99}\). Illustrate by graphing \(f\) and the tangent line.
ANSWER:Step 1 of 4
The rule of the derivatives are \(\frac{d}{d x}(c)=0,\ \frac{d}{d x}[c f(x)]=c f^{\prime}(x),\ \frac{d}{d x}\left(x^{n}\right)=n x^{n-1},\ \frac{d}{d x}[f(x)+g(x)]=f^{\prime}(x)+g^{\prime}(x)\), etc.