edited by
532 views
2 votes
2 votes

If $f_{n}(x)$ are continuous functions from [0, 1] to [0, 1], and $f_{n}(x)\rightarrow f(x)$ as $n\rightarrow \infty $, then which of the following statements is true?

  1. $f_{n}(x)$ converges to $f(x)$ uniformly on [0, 1]
  2. $f_{n}(x)$ converges to $f(x)$ uniformly on (0, 1)
  3. $f(x)$ is continuous on [0, 1]
  4. None of the above
edited by

Please log in or register to answer this question.

Related questions

2 votes
2 votes
1 answer
1
makhdoom ghaya asked Oct 15, 2015
1,550 views
Define $\left \{ x_{n} \right \}$ as $x_{1}=0.1,x_{2}=0.101,x_{3}=0.101001,\dots$ Then the sequence $\left \{ x_{n} \right \}$.Converges to a rational numberConverges to ...
2 votes
2 votes
1 answer
2
makhdoom ghaya asked Oct 11, 2015
613 views
Let $U_{n}=\sin(\frac{\pi }{n})$ and consider the series $\sum u_{n}$. Which of the following statements is false?$\sum u_{n}$ is convergent$u_{n}\rightarrow 0$ as $n\rig...
2 votes
2 votes
3 answers
3
Arjun asked Oct 11, 2015
800 views
The series $$\sum ^{\infty }_{n=1}\frac{(-1)^{n+1}}{\sqrt{n}}$$ Converges but not absolutely. Converges absolutely. Diverges. None of the above.
3 votes
3 votes
2 answers
4
Arjun asked Oct 12, 2015
1,041 views
The function $f(x)$ defined by $$f(x)= \begin{cases} 0 & \text{if x is rational } \\ x & \text{if } x\text{ is irrational } \end{cases}$$is not continuous at any po...