l****y
发帖数: 92 | 1 let f(x) be a function defined for all x from an interval (c,d) containing a
point x0. suppose that f(x) is continuous at the point x0, and f(x0)/=0 (
does not equal to 0), which of the following is true?
a) there exists a neighborhood (x0-a,x0+a), a>0, of the point x0 at whose
all points fulfill the inequality |f(x)|>f(x0)/2
b) for each a>0, the inequality |f(x)|>a*f(x0) is true for all x belongs to
(x0-a,x0+a)
c) for each number M strictly greater than |f(x0)|, there exists a
neighborhood N=(x | l****y
发帖数: 92 | 2 i know (a) is right, (b) is wrong, how to prove (c) is right? | s*x
发帖数: 3328 | 3 g(x)=M-f(x)
g(x_0)>0
【在 l****y 的大作中提到】
: i know (a) is right, (b) is wrong, how to prove (c) is right?
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