[分析] 數值分析的證明

[WaterPisces ( )]

Let f€ C[a,b],and let p be in the open interval (a,b).

a. Suppose f(p) =/= 0. Show that a δ> 0  exists with f(x) =/= 0

   for all x in  [p-δ,p+δ],where [p-δ,p+δ] a subset of [a,b].

b. Suppose f(p) = 0 and k > 0 is given. Show that a δ> 0  exists with

  ｜f(x)｜=< k  for all x in  [p-δ,p+δ],where [p-δ,p+δ] a subset of [a,b].


thx

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