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lim-x-x-cos-x-x-sin-x-




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

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