- #1

Ka Yan

- 27

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**Two questions need helps**

I got two questions below need helps:

1. Let f be a real continuous function defined on a closed subset E of R[tex]^1[/tex], then how can I prove the existence of some corressponding real continuous functions g on R[tex]^1[/tex], such that g(x)=f(x) for all x[tex]\in[/tex]E ?

2. Let f and g two functions defined on R[tex]^2[/tex] by: f(0,0)=g(0,0)=0, f(x,y)=xy[tex]^2[/tex]/(x[tex]^2[/tex]+y[tex]^4[/tex]), and g(x,y)=xy[tex]^2[/tex]/(x[tex]^2[/tex]+y[tex]^6[/tex]), if (x,y)[tex]\neq[/tex](0,0). Then how can I prove that: (1) f is bounded on R[tex]^2[/tex], and (2) g is unbounded in every neighborbood of (0,0) ?

Thks!

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