Recent content by Cephal

  1. C

    MHB How is the proof of the hard limit problem related to continuity of a function?

    Thank you very very much $$\chi\sigma$$.(Clapping)
  2. C

    MHB How is the proof of the hard limit problem related to continuity of a function?

    Thank you Opalg for your answer. In fact I have already proved that: $$\displaystyle \lim_{n\to+\infty} n\int_{0}^1 x^ng(x)\mathrm{d}x=g(1)$$ with $$g \in\mathcal{C}^0(\left[0,1\right],\mathbb{R})$$.My problem is to prove this: $$\displaystyle \int_0^1 x^n...
  3. C

    MHB How is the proof of the hard limit problem related to continuity of a function?

    Hello everybody, I have proved that: $$\displaystyle \lim_{n\to+\infty} n\int_{0}^1 x^ng(x)\mathrm{d}x=g(1)$$ with $$g \in\mathcal{C}^0(\left[0,1\right],\mathbb{R})$$.But I don't know how to prove this: $$\displaystyle \int_0^1 x^n...