TIFR ECE 2011 | Question: 4

Question

Let $\lim _{n \rightarrow \infty} x_{n}=x$. Then which of the following is $\text{TRUE.}$

• A. There exists an $n_{0}$, such that for all $n>n_{0},\left|x_{n}-x\right|=0$.
• B. There exists an $n_{0}$, such that for all $n>n_{0},\left|x_{n}-x\right| \leq \epsilon$ for any $\epsilon>0$.
• C. For every $\epsilon>0$, there exists an $n_{0}$, such that for all $n>n_{0},\left|x_{n}-x\right| \leq \epsilon$.
• D. There exists an $n_{0}$, such that for all $n>n_{0},\left|\frac{x_{n}}{x}\right| \leq \epsilon$ for any $\epsilon>0$.
• E. None of the above.