$(5)$ Use $a(logically$ chosen$)$ linear approximation $off(x,y)=\sqrt[\phantom{2}]{x+y^3}to$ estimate

$\sqrt[\phantom{2}]{1\mathrm{.}02+{1\mathrm{.}99}^3}.$ Use a calculator $to$ compute $\sqrt[\phantom{2}]{1\mathrm{.}02+{1\mathrm{.}99}^3}$ and compare the result

$to$ the approximation. $(The$ approximation better $be$ pretty close $to$ the calculator

value!$)$