- #1

murshid_islam

- 442

- 17

- TL;DR Summary
- A question about limit

[tex]\lim_{x \rightarrow 1} \frac{x^2 - 1}{x-1}[/tex]

For this, we first divide the numerator and denominator by [itex](x-1)[/itex] and we get

[tex]\lim_{x \rightarrow 1} (x+1)[/tex]

Apparently, we can divide by [itex](x-1)[/itex] because [itex]x \neq 1[/itex], but then we plug in [itex]x = 1[/itex] and get 2 as the limit. Is [itex]x = 1[/itex] or [itex]x \neq 1[/itex]? What exactly is happening here?

For this, we first divide the numerator and denominator by [itex](x-1)[/itex] and we get

[tex]\lim_{x \rightarrow 1} (x+1)[/tex]

Apparently, we can divide by [itex](x-1)[/itex] because [itex]x \neq 1[/itex], but then we plug in [itex]x = 1[/itex] and get 2 as the limit. Is [itex]x = 1[/itex] or [itex]x \neq 1[/itex]? What exactly is happening here?