Test1

$latex \begin{array}{l}1.\,\,\text{Using}\,\,\text{the}\,\,\text{picture}\,\,\text{above,}\,\,\underset{x\to A}{\mathop{\lim }}\,F(x)\,=\,2.\,\,\text{The}\,\,\text{limit}\,\,\text{is}\,\,\text{the}\,\,\text{value}\,\,\text{the}\,\,\text{function}\,\,\text{APPROACHES}\,\,\text{at}\,\,\text{the,}\,\,\\\text{given}\,\,\text{point}\,\,\text{not}\,\,\text{necessarily}\,\,\text{the}\,\,\text{value}\,\,\text{of}\,\,\text{the}\,\,\text{function}\,\,\text{at}\,\,\text{the}\,\,\text{point.}\,\,\text{It}\,\,\text{makes}\,\,\text{no difference}\\\text{that}\,\,\text{the}\,\,\text{value}\,\,\text{of the}\,\,\text{function}\,\,\text{equals}\,\,\text{5,}\,\,\text{only}\,\,\text{what}\,\,\text{the}\,\,\text{function}\,\,\text{approaches}\,\,\text{from}\,\,\text{both}\,\,\text{sides.}\end{array}$









$latex \begin{array}{l}2.\,\,\text{Using}\,\,\text{the}\,\,\text{picture}\,\,\text{above}\,\,\underset{x\to {{A}^{-}}}{\mathop{\lim }}\,\,G(x)\,=1\,\,\text{and}\,\,\underset{x\to {{A}^{+}}}{\mathop{\lim }}\,\,G(x)\,=3.\,\,\text{There}\,\,\text{exists}\,\,\text{a}\,\,\text{limit}\,\,\text{from}\,\,\text{each}\,\,\text{side,}\,\,\text{however}\,\text{since}\,\,\text{the}\,\,\text{two}\,\,\text{limits}\\\text{are}\,\,\text{different}\,\,\underset{x\to {{A}^{-}}}{\mathop{\lim }}\,\,G(x)\,\ne \underset{x\to {{A}^{+}}}{\mathop{\lim }}\,\,G(x)\,,\,\,\text{no}\,\,\text{limit}\,\,\text{exists}\,\,\text{at}\,\text{A,}\,\\\text{written}\,\,\underset{x\to A}{\mathop{\lim }}\,\,\,G(x)\,\,\text{does}\,\,\text{not}\,\,\text{exist.}\end{array}$