PART 3：例題-開平方根

試以微分公式估計 \(\sqrt {144.01} \) 之近似值

SOL:

(1)設 \(f(x) = \sqrt x \) ， \(f'(x) = \frac{1}{{2\sqrt x }}\)

(2)微分公式 \(f(x + \Delta x) \buildrel\textstyle.\over= f(x) + f'(x)\Delta x\)

(3)令 \(x = 144\) ， \(\Delta x = 0.01\)

\(f(144 + 0.01) \buildrel\textstyle.\over= f(144) + f'(144)\left( {0.01} \right)\)

\(f(144.01) \buildrel\textstyle.\over= 12 + \frac{1}{{24}}\left( {0.01} \right)\) \( = 12.000416\)