Question

高等数学 极限 画横线的两步怎样理解

Answer 1

令 h(x) = (1/2) * [ f(x) + g(x) + / f(x) - g(x) / ]
1 ） f(x) ≥ g(x) 时，
h(x) = (1/2) * [ f(x) + g(x) + / f(x) - g(x) / ]
= (1/2) * [ f(x) + g(x) + （ f(x) - g(x) ）]
= f(x)
2 ） f(x) ≤ g(x) 时，
h(x) = (1/2) * [ f(x) + g(x) + / f(x) - g(x) / ]
= (1/2) * [ f(x) + g(x) -（ f(x) - g(x) ）]
= g(x)
故 max { f(x), g(x) } = h(x) = (1/2) * [ f(x) + g(x) + / f(x) - g(x) / ]