Question Number 221347 by RoseAli last updated on 31/May/25
$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{4}−{x}^{\mathrm{2}} }{{x}−\mathrm{2}} \\ $$
Answered by AntonCWX8 last updated on 31/May/25
$$\frac{\mathrm{4}−{x}^{\mathrm{2}} }{{x}−\mathrm{2}} \\ $$$$=\frac{\left(\mathrm{2}+{x}\right)\left(\mathrm{2}−{x}\right)}{{x}−\mathrm{2}} \\ $$$$=\frac{\left(\mathrm{2}+{x}\right)\left(−\mathrm{1}\right)\left({x}−\mathrm{2}\right)}{{x}−\mathrm{2}} \\ $$$$=−\mathrm{1}\left(\mathrm{2}+{x}\right) \\ $$$$ \\ $$$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\left(−\left(\mathrm{2}+{x}\right)\right)=−\mathrm{4} \\ $$