515. Calculate approximately $1.998^{5}$.
Solution. Consider the function $f(x)=x^{5}$. Here $x_{1}=1.998$, $x_{0}=2, \quad \Delta x=-0.002, f\left(x_{1}\right)=f(1.998)=1.998^{5}$. Next, we find $f\left(x_{0}\right)=$ $=f(2)=2^{5}=32, f^{\prime}\left(x_{0}\right) \Delta x=5 \cdot 2^{4}(-0.002)=5 \cdot 16(-0.002)=-0.16$.

As a result, we get $1.998^{5} \approx 32-0.16=31.84$.