Suppose f : D → R. Using only the defnition of limit of a function, show that if $\lim_{x\rightarrow x_0} f(x)=L>0$ then there is a number $d>0$ such that $f(x)≥L/2$ for all $x \in (x_0 −d,x_0 +d) \cap D$.
I' m not really sure where to go after writing down the definition of the limit for the assumption. Thanks in advance.