Question

The approximate value of ${\left(1.999\right)}^5$ is

• A. 31.92
• B. 31.82
• C. 31.72
• D. 31.62

Answer 1

The correct option is A 31.92

Let $y=x^{5}Letx=2and\Delta x=-0.001\frac{dy}{dx}=5x^4\Delta y=\frac{dy}{dx}\Delta x\Rightarrow \Delta y=5x^4\times \left(-0.001\right)\Rightarrow {\left(\Delta y\right)}_{x=2}=5{\left(2\right)}^4\times \left(-0.001\right)=-0.08y=(2{)}^5=32\therefore {\left(1.999\right)}^5=y+\Delta y=31.92$