Question Number 80296 by john santu last updated on 02/Feb/20
$${what}\:{is}\:{the}\:{value}\:{of}\: \\ $$$$\underset{{x}\rightarrow−\infty\:} {\mathrm{lim}}\:{e}^{\frac{\mathrm{6}{x}^{\mathrm{2}} +{x}}{\mathrm{3}{x}+\mathrm{5}}} \:? \\ $$$$\mathrm{0}\:{or}\:\infty\:? \\ $$
Commented by Tony Lin last updated on 02/Feb/20
$${let}\:{t}=−{x} \\ $$$$\underset{{t}\rightarrow+\infty} {\mathrm{lim}}{e}^{\frac{\mathrm{6}{t}^{\mathrm{2}} −{t}}{\mathrm{5}−\mathrm{3}{t}}} \\ $$$$={e}^{\underset{{t}\rightarrow+\infty} {\mathrm{lim}}\frac{\mathrm{6}{t}^{\mathrm{2}} −{t}}{\mathrm{5}−\mathrm{3}{t}}} \: \\ $$$$\underset{{t}\rightarrow+\infty} {\mathrm{lim}}\frac{\mathrm{6}{t}^{\mathrm{2}} −{t}}{\mathrm{5}−\mathrm{3}{t}}=\underset{{t}\rightarrow+\infty} {\mathrm{lim}}\frac{\mathrm{12}{t}−\mathrm{1}}{−\mathrm{3}}=−\infty \\ $$$${e}^{−\infty} =\mathrm{0} \\ $$
Commented by jagoll last updated on 02/Feb/20
Commented by jagoll last updated on 02/Feb/20
$${good} \\ $$