Linear Approximation

  1. Find the linearization, \(L(x)\), of the function at given \(x=a\).

    2. (a) \( f(x)=\ln x, \quad  x=1\)    solution

    (b) \( f(x)=\sqrt{x+3}, \quad  x=1\)   solution 

  2. Use a linear approximation to estimate the given number.

    3. (a) \( (4.01)^{\frac{1}{2}}\)   solution

    (b) \( \sqrt[3] {27.1}\)  solution 

  3. Use a linear approximation to approximate the value of \( e^{0.2} \).   solution

  4. Use a linear approximation to estimate \( (1.01)^3 \).   solution

  5. Find a linearization, \(L(x)\), of the function \(f(x)=\sqrt{1+x} \) at \(x=0\). Use it to approximate the following numbers.   solution

    6.   (a) \(\sqrt{1.03} \)     (b) \(\sqrt{0.98} \)