(Solved): A function \( f(x) \), a point \( x_{0} \), the limit of \( f(x) \) as \( x \) approaches \( x_{0} ...

A function \( f(x) \), a point \( x_{0} \), the limit of \( f(x) \) as \( x \) approaches \( x_{0} \), and a positive number \( \varepsilon \) is given. Find a number \( \delta>0 \) such that for all \( x, 0<\left|x-x_{0}\right|<\delta \Rightarrow \) \( |f(x)-L|<\varepsilon \). Round to six decimal places as needed. \( f(x)=2 x+1, L=7, x_{0}=3 \), and \( \varepsilon=0.01 \) A. \( 0.025000 \) B. \( 0.010000 \) C. \( 0.003333 \) D. \( 0.005000 \)