Вычислите (корень4,008-корень0,996)^15.

[latex] \sqrt{4.008} \\ f(x+\Delta x)=f(x)+f'(x)*\Delta x \\ f(x)= \sqrt{x} \\ f'(x)= \frac{1}{2 \sqrt{x} } \\ f(4+0,008)=f(4)+f'(4)*0,008=2+0.25*0.008=2.002 \\ \\ \\ \sqrt{0.996} \\ f(x+\Delta x)=f(x)+f'(x)*\Delta x \\ f(x)= \sqrt{x} \\ f'(x)= \frac{1}{2 \sqrt{x} } \\ f(1-0.004)=f(1)+f'(1)*(- \Delta x)=1-0.5*0.004=0.998 \\ \\ \\ (2.002-0.998)^{15}={1.004}^{15} \\ (x+ \Delta x)^n = x^n+n*x^{n-1}*\Delta x==\ \textgreater \ \\ (1+0.004)^{15}=1^{15}+15*1^{14}*0.004=1+15*0.004=1.06[/latex]