Linear Approximation

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

(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.

(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