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在文[1]中,笔者曾介绍了绝对值|f(x)|的零点分区直观法:绝对值|f(x)|的零点a_i(i=1,2,…,n),把函数f(x)的定义域(a,b),分为n+1个区间(a,a_1)、[a_1,a_2]、[a_2,a_3]、…、[a_(n-1),a_n]、[a_n,b]。(其中a_(i-1)0),确定|f(x)|的值。也就是说,由[a_(i-1),a_i]内f(x)的符号,就可以确定在[a_(i-1),a_i]内的|f(x)|的值。 本文试将此法推广到平面上,来解决含x、y的绝对值|f(x、y)|的有关问题。
In the paper [1], I introduced the zero-point visualization of the absolute value | f (x) |: the zero point a_i (i = 1,2, ..., n) of the absolute value | f (a, b) is divided into n + 1 intervals (a, a_1), [a_1, a_2], [a_2, a_3], ..., [a_ (n-1), a_n] , [A_n, b]. (Where a_ (i-1) 0), the value of | f (x) | is determined. That is, the value of | f (x) | within [a_ (i-1), a_i] can be determined from the sign of f (x) in [a_ (i-1), a_i]. This paper tries to generalize this method to the plane, to solve the problem with the absolute value of x, y | f (x, y) |.