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Question Number 184901 by mathlove last updated on 13/Jan/23

$$\underset{\frac{2}{x}\to 2}{\lim }\frac{100+x}{101x}$$

Commented by SEKRET last updated on 13/Jan/23

$$\mathbf{x}\to 1$$

Answered by cortano2 last updated on 13/Jan/23

$${lim}_{t\to 2}\frac{100+\frac{2}{t}}{101\left(\frac{2}{t}\right)}=\frac{101}{101}=1$$

Answered by alephzero last updated on 13/Jan/23

$$\underset{\frac{2}{x}\to 2}{\lim }\frac{100+x}{101x}$$$$\frac{2}{x}\to 2$$$$\Rightarrow x\to 1$$$$\Rightarrow \underset{\frac{2}{x}\to 2}{\lim }\frac{100+x}{101x}=\underset{x\to 1}{\lim }\frac{100+x}{101x}=$$$$=\frac{100+1}{101\cdot 1}=\frac{101}{101}=1$$

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