Question

x-1/x as x approaches 0

Answer 1

\[\lim_{x \rightarrow 0}\frac{ x-1 }{x} = \]
knowing that we can't divide by 0, the limit would be an indetermination.

Answer 2

But wouldnt it be infinite since o approaches 0

Answer 3

Wrong, this is not an indeterminate form: \[
\frac {-1}0
\]We know that this is undefined!

Answer 4

Consider \[
x\times 0=-1
\]It is not like \[
x\times 0=0
\]

Answer 5

In the first equation, there is NO defined number that could be a solution for \(x\).
Hence undefined.

In the second equation there a many possible solutions for \(x\) and we don't have the context to determine which is correct.
Hence indeterminate.

Answer 6

This limit does not exist. It can approach \(-\infty\) or \(\infty\) depending which side you come from.

Answer 7

Nicely said @wio

Answer 8

oh got it but the beginning was kind of unclear but thanks