- #1

MichPod

- 231

- 45

Hello. Per what I was taught in my youth, ##\lim_{x \to 0}\frac{1}{x}=\infty##

Is it in agreement with how the calculus is taught today in the High Schools and Universities of US/Canada specifically?

Per what my son says, that limit should be considered as undefined because

##\lim_{x \to 0^+}\frac{1}{x}=+\infty##

and

##\lim_{x \to 0^-}\frac{1}{x}=-\infty##

and as these infinities have different signs, the general limit does not exist (even if expressed as "infinity").

Disclaimer: I understand that my question is about the conventions and about how the math is taught, not about the math itself.

Is it in agreement with how the calculus is taught today in the High Schools and Universities of US/Canada specifically?

Per what my son says, that limit should be considered as undefined because

##\lim_{x \to 0^+}\frac{1}{x}=+\infty##

and

##\lim_{x \to 0^-}\frac{1}{x}=-\infty##

and as these infinities have different signs, the general limit does not exist (even if expressed as "infinity").

Disclaimer: I understand that my question is about the conventions and about how the math is taught, not about the math itself.

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