Question Number 78828 by john santu last updated on 21/Jan/20
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}+\mathrm{sin}\:{x}\right).{lnx}\:=\:? \\ $$
Commented by mr W last updated on 21/Jan/20
$$\left(\mathrm{2}+\mathrm{sin}\:{x}\right).{lnx}\:>\mathrm{ln}\:{x} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{2}+\mathrm{sin}\:{x}\right).{lnx}\:>\underset{{x}\rightarrow\infty} {\mathrm{lim}ln}\:{x}=\infty \\ $$$$\Rightarrow\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{2}+\mathrm{sin}\:{x}\right).{lnx}\:=\infty \\ $$
Commented by john santu last updated on 21/Jan/20
$${sir}\:{in}\:{my}\:{book}\:,\:{the}\:{answer}\:{is}\: \\ $$$${ln}\:\mathrm{3}.\:{i}'{m}\:{can}'{t}\:{get}\:{it} \\ $$
Commented by mr W last updated on 21/Jan/20
$${either}\:{the}\:{question}\:{is}\:{wrong}\:{or}\:{the} \\ $$$${answer}\:{in}\:{your}\:{book}\:{is}\:{wrong}. \\ $$