let $\displaystyle f(x)$be continuous on $\displaystyle [ 0,\infty )$. Define $\displaystyle L=\{z\in R \ni \exists$ $\displaystyle a$ $\displaystyle sequence$ $\displaystyle x_n \rightarrow \infty$ $\displaystyle and$ $\displaystyle f(x_n) \rightarrow z$ $\displaystyle as$ $\displaystyle n \rightarrow \infty\}$

Prove a) $\displaystyle L$ is closed b)$\displaystyle L$ is connected c)$\displaystyle L$ is an interval