Question Number 79064 by Khyati last updated on 22/Jan/20
$${find}\:\:{li}\underset{{x}\rightarrow\:−\mathrm{3}} {{m}}\frac{{x}^{\mathrm{3}} +\mathrm{27}}{{x}^{\mathrm{5}} +\mathrm{243}} \\ $$
Answered by john santu last updated on 22/Jan/20
$$\underset{{x}\rightarrow−\mathrm{3}} {\mathrm{lim}}\frac{\frac{{d}}{{dx}}\left({x}^{\mathrm{3}} +\mathrm{27}\right)}{\frac{{d}}{{dx}}\left({x}^{\mathrm{5}} +\mathrm{243}\right)}\:=\:\underset{{x}\rightarrow−\mathrm{3}} {\mathrm{lim}}\:\frac{\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{5}{x}^{\mathrm{4}} }=\frac{\mathrm{3}}{\mathrm{5}×\mathrm{9}} \\ $$$$\frac{\mathrm{1}}{\mathrm{15}} \\ $$
Commented by Khyati last updated on 23/Jan/20
$${solve}\:{without}\:{LHospital}\:{rule} \\ $$
Commented by john santu last updated on 23/Jan/20
$${using}\:{Horner}\:{method}\:{sir} \\ $$
Commented by john santu last updated on 23/Jan/20
$$\underset{{x}\rightarrow−\mathrm{3}} {\mathrm{lim}}\:\frac{\left({x}+\mathrm{3}\right)\left({x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{9}\right)}{\left({x}+\mathrm{3}\right)\left({x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{3}} +\mathrm{9}{x}^{\mathrm{2}} −\mathrm{27}{x}+\mathrm{81}\right)} \\ $$$$\underset{{x}\rightarrow−\mathrm{3}\:} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{9}}{{x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{3}} +\mathrm{9}{x}^{\mathrm{2}} −\mathrm{27}{x}+\mathrm{81}} \\ $$
Commented by Khyati last updated on 23/Jan/20
$${Horner}\:{Method}\:????? \\ $$