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Question Number 152211 by nitu last updated on 26/Aug/21

$$\underset{x\to 0}{\lim }\frac{1}{{\mathrm{x}}^2}$$$$\mathrm{should}\mathrm{the}\mathrm{answer}\mathrm{be}\mathrm{\infty }\mathrm{or}\mathrm{is}\mathrm{it}\mathrm{DNE}.$$$$\mathrm{my}\mathrm{main}\mathrm{question}\mathrm{is},$$$$\mathrm{when},$$$$\underset{x\to \mathrm{a}}{\lim }\mathrm{f}\left(\mathrm{x}\right)=\mathrm{\infty }$$$$\mathrm{does}\mathrm{it}\mathrm{not}\mathrm{exist}?\mathrm{is}\mathrm{it}\mathrm{DNE}?$$

Commented by MJS_new last updated on 26/Aug/21

$$\underset{x\to 0}{\lim }\frac{1}{x}\mathrm{does}\mathrm{not}\mathrm{exist}\mathrm{because}\underset{x\to 0^{-}}{\lim }\frac{1}{x}\ne \underset{x\to 0^{+}}{\lim }\frac{1}{x}$$$$\underset{x\to 0}{\lim }\frac{1}{x^2}=+\mathrm{\infty }$$$$\mathrm{obviously}{\mathrm{there}}^{\prime }\mathrm{s}\mathrm{a}\mathrm{difference}...$$

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