Limx - > 1 (1 / x) = 1 prove limit by definition |1/x-1|

Limx - > 1 (1 / x) = 1 prove limit by definition |1/x-1|

General division | 1 / X-1 | = | (1-x) / X |, because X - > 1, it can be limited to 1 / 2

Prove limx → 2 = 1 / X-1 = 1 with the limit definition of function
When we get (X-2) / (x-1), we might as well limit the range of X to (X-2) < 1 / 2 Why?
Another problem is limx → 1 (x ^ 2-1) / (x ^ 2-x) = 2. When we get (x-1) / x, let (x-1)

Because x → 2, we consider that x is near 2. The purpose of restriction is to solve the denominator X-1 and enlarge it
|1 / (x-1) - 1 | = | (X-2) / (x-1) |, now the molecule is | X-2 |, the denominator | X-1 |, if you want to reduce it to a number, you have to limit | X-2 ||