[微積] 兩題微積分

[dreamingaway (Wherever I May Roam)]

1. Define a function f:R→R by f(x)=0 if x belongs to R\Q,
  and f(x)=1/p if x=q/p where p,q belong to Z, p≧1 and gcd{p,q}=1.
  Show that lim f(x)=0
            x→1/2

2. Let f,g:[0,1]→R, be continuous functions. Define h(x)=max{f(x),g(x)}
  for all x belong to [0,1]. Show that h(x) is also a continuous function.

請問這2題要怎麼做  謝謝

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推 GaussQQ     :第一題可用定義
→ GaussQQ     :第二題用h(x)=1/2{f(x)+g(x)+|f(x)-g(x)|}