Question Number 187029 by yaslm last updated on 12/Feb/23
Answered by cortano12 last updated on 12/Feb/23
$$\:\left(\mathrm{1}\right)\:\underset{{x}\rightarrow−\mathrm{2}^{−} } {\mathrm{lim}}\:\left({ax}+{b}\right)=\:\underset{{x}\rightarrow−\mathrm{2}^{+} } {\mathrm{lim}}\left({x}^{\mathrm{2}} +\mathrm{2}{b}−\mathrm{17}\right) \\ $$$$\:\:\:\:\:\:\:−\mathrm{2}{a}+{b}\:=\:\mathrm{4}+\mathrm{2}{b}−\mathrm{17} \\ $$$$\:\:\:\:\:\:\:−\mathrm{2}{a}−{b}\:=−\mathrm{13} \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{1}^{−} } {\mathrm{lim}}\:\left({x}^{\mathrm{2}} +\mathrm{2}{b}−\mathrm{17}\right)=\underset{{x}\rightarrow\mathrm{1}^{+} } {\mathrm{lim}}\:\left(\mathrm{3}{x}−\mathrm{3}+{a}\right) \\ $$$$\:\:\:\:\:\:\:\mathrm{1}+\mathrm{2}{b}−\mathrm{17}\:=\:\mathrm{3}−\mathrm{3}+{a} \\ $$$$\:\:\:\:\:\:\:\:−{a}+\mathrm{2}{b}\:=\:\mathrm{16}\Rightarrow{a}=\mathrm{2}{b}−\mathrm{16} \\ $$$$\Rightarrow−\mathrm{2}\left(\mathrm{2}{b}−\mathrm{16}\right)−{b}=−\mathrm{13} \\ $$$$\Rightarrow−\mathrm{5}{b}\:=\:−\mathrm{45}\:\Rightarrow\begin{cases}{{b}=\mathrm{9}}\\{{a}=\mathrm{2}}\end{cases} \\ $$