Question Number 184901 by mathlove last updated on 13/Jan/23
$$\underset{\frac{\mathrm{2}}{{x}}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{100}+{x}}{\mathrm{101}{x}} \\ $$
Commented by SEKRET last updated on 13/Jan/23
$$\boldsymbol{\mathrm{x}}\rightarrow\mathrm{1} \\ $$
Answered by cortano2 last updated on 13/Jan/23
$${lim}_{{t}\rightarrow\mathrm{2}} \frac{\mathrm{100}+\frac{\mathrm{2}}{{t}}}{\mathrm{101}\left(\frac{\mathrm{2}}{{t}}\right)}=\frac{\mathrm{101}}{\mathrm{101}}=\mathrm{1} \\ $$
Answered by alephzero last updated on 13/Jan/23
$$\underset{\frac{\mathrm{2}}{{x}}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\mathrm{100}+{x}}{\mathrm{101}{x}} \\ $$$$\frac{\mathrm{2}}{{x}}\rightarrow\mathrm{2} \\ $$$$\Rightarrow\:{x}\rightarrow\mathrm{1} \\ $$$$\Rightarrow\:\underset{\frac{\mathrm{2}}{{x}}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{\mathrm{100}+{x}}{\mathrm{101}{x}}\:=\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{100}+{x}}{\mathrm{101}{x}}\:= \\ $$$$=\:\frac{\mathrm{100}+\mathrm{1}}{\mathrm{101}\:\centerdot\:\mathrm{1}}\:=\:\frac{\mathrm{101}}{\mathrm{101}}\:=\:\mathrm{1} \\ $$