#### Problem 83E

83. (a) Find the linearization of $f(x)=\sqrt[3]{1+3 x}$ at $a=0$. State the corresponding linear approximation and use it to give an approximate value for $\sqrt[3]{1.03}$.

(b) Determine the values of $x$ for which the linear approximation given in part (a) is accurate to within $0.1$.