求数学达人解答微积分相关的题目啊TT.

Question

如题所述

Answer 1

参考函数为f(x)=x^(-1/2),f'(x)=(-1/2)x^(-3/2)
参考点为x0=100
所以
f(99.9)=f(100-0.1)≈f(100)-0.1*f'(100)
≈1/10-0.1*(-1/2)*(100)^(-3/2)
≈0.1+0.1*0.5*0.001
≈0.10005

Answer 2

这样的题目，就是在该点作线性近似，用切线代替函数曲线
f(x) = x (-1/2) (幂次)
f(100) - f(99.9) = f'(100) * (100 - 99.9)
求f’(100) = (-1/2) * (100) (-3/2) (幂次) = - 1/2000 = - 0.0005
所以 f(99.9) = 1/10 - (-0.005)*(0.1) = 0.10005

Answer 3