Question Number 134746 by zahaku last updated on 06/Mar/21
$${How}\:{to}\:{calculate} \\ $$$${li}\underset{{x}\rightarrow−\mathrm{3}} {{m}}\frac{{x}+\mathrm{3}}{\:\sqrt{\mid{x}^{\mathrm{2}} +{x}−\mathrm{6}\mid}}\:\:\:\:? \\ $$
Answered by mathmax by abdo last updated on 06/Mar/21
$$\mathrm{0} \\ $$
Answered by EDWIN88 last updated on 07/Mar/21
$$\underset{{x}\rightarrow−\mathrm{3}} {\mathrm{lim}}\:\frac{\left(\mathrm{x}+\mathrm{3}\right)}{\:\sqrt{\mid\left(\mathrm{x}+\mathrm{3}\right)\left(\mathrm{x}−\mathrm{2}\right)\mid}}\:=\:\underset{{x}\rightarrow−\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}−\mathrm{x}}}\:.\underset{{x}\rightarrow−\mathrm{3}} {\mathrm{lim}}\:\frac{\left(\mathrm{x}+\mathrm{3}\right)}{\:\sqrt[{\mathrm{4}}]{\left(\mathrm{x}+\mathrm{3}\right)^{\mathrm{2}} }} \\ $$$$=\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{5}}}.\underset{{x}\rightarrow−\mathrm{3}} {\mathrm{lim}}\sqrt{\mathrm{x}+\mathrm{3}}\:=\:\mathrm{0} \\ $$$$ \\ $$