Monday, June 3, 2019

calculus - I'm trying to show that limlimitsxrightarrowinftyfrac1x=0, is my argument ok?

Here is my try:



We know that lim, so define y=\frac{1}{x}, then:



\lim\limits_{x \rightarrow \infty}\frac{1}{x} = \lim\limits_{y\rightarrow 0}\frac{1}{\frac{1}{y}}= \lim\limits_{y \rightarrow 0} 1 \frac{y}{1}=\lim\limits_{y \rightarrow 0} y = 0




Is my argument correct? I don't know if it's right or wrong.



If it's ok, how do I justify each step?



If it's wrong, which step is illegal?



Thanks.

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