Question Number 41998 by Joel578 last updated on 16/Aug/18
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{{x}\:+\:\mathrm{cos}\:{x}}{{x}\:+\:\mathrm{sin}\:{x}} \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 16/Aug/18
$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}+\frac{{cosx}}{{x}}}{\mathrm{1}+\frac{{sinx}}{{x}}} \\ $$$${the}\:{value}\:{of}\:{sinx}\:{lies}\:{in}\:{between}\:\pm\mathrm{1}\:{whatever} \\ $$$${the}\:{value}\:{of}\:{x} \\ $$$${similarly}\:{the}\:{value}\:{of}\:{cosx}\:{lies}\:{in}\:{bdtween}\pm\mathrm{1} \\ $$$${whatever}\:{the}\:{value}\:{of}\:{x} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}+\mathrm{0}}{\mathrm{1}+\mathrm{0}}=\mathrm{1} \\ $$$$ \\ $$