Question

HELP PLEASE, Part a of the question was posted earlier on.

Answer 1

$\bf \lim\limits_{x\to 6}~\cfrac{x^2+x+42}{x-6}\implies \lim\limits_{x\to 6}~\cfrac{(x+7)(x-6)}{(x-6)}\implies \lim\limits_{x\to 6}~x+7 \\\\\\ \lim\limits_{x\to 6}~(6)+7=13 \\\\\\ \textit{since the original equation holds for all, }x\ne 6,\textit{ then it approaches}\\ \textit{the same limit as }x+7$