Linear Approximation
1. Find the linearization, \(L(x)\), of the function at given \(x=a\).
(a) \( f(x)=\ln x, \quad x=1\)
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(b) \( f(x)=\sqrt{x+3}, \quad x=1\)
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2. Use a linear approximation to estimate the given number.
(a) \( (4.01)^{\frac{1}{2}}\)
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(b) \( \sqrt[3] {27.1}\)
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3. Use a linear approximation to approximate the value of \( e^{0.2} \).
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4. Use a linear approximation to estimate \( (1.01)^3 \).
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