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Question Number 65013 by Rio Michael last updated on 24/Jul/19

why do we divide each term by n when given the question  lim_(x→∞)   ((3 +2n)/(1+n)) ?

$${why}\:{do}\:{we}\:{divide}\:{each}\:{term}\:{by}\:{n}\:{when}\:{given}\:{the}\:{question} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\:\frac{\mathrm{3}\:+\mathrm{2}{n}}{\mathrm{1}+{n}}\:? \\ $$

Answered by Tanmay chaudhury last updated on 24/Jul/19

lim_(n→∞)  (((3/n)+2)/((1/n)+1))  =((0+2)/(0+1))=2   [we devide N_r  and D_r  by highest power  n  to get 0(zero)   because   (1/∞)→0]

$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\frac{\mathrm{3}}{{n}}+\mathrm{2}}{\frac{\mathrm{1}}{{n}}+\mathrm{1}} \\ $$$$=\frac{\mathrm{0}+\mathrm{2}}{\mathrm{0}+\mathrm{1}}=\mathrm{2}\:\:\:\left[{we}\:{devide}\:{N}_{{r}} \:{and}\:{D}_{{r}} \:{by}\:{highest}\:{power}\right. \\ $$$$\left.{n}\:\:{to}\:{get}\:\mathrm{0}\left({zero}\right)\:\:\:{because}\:\:\:\frac{\mathrm{1}}{\infty}\rightarrow\mathrm{0}\right] \\ $$

Commented by Rio Michael last updated on 24/Jul/19

thanks, at times i just think of infinity as a number

$${thanks},\:{at}\:{times}\:{i}\:{just}\:{think}\:{of}\:{infinity}\:{as}\:{a}\:{number} \\ $$

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