Question

Lim
x →1+. 1- x/x² - 1

Answer 1

Answer:
`\displaystyle \boldsymbol{-(1)/(2)}`

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Work Shown:

`\displaystyle L = \lim_{\text{x}\to 1^(+)} \frac{1-\text{x}}{\text{x}^2-1}\\\\\\\displaystyle L = \lim_{\text{x}\to 1^(+)} \frac{-(\text{x}-1)}{(\text{x}-1)(\text{x}+1)}\\\\\\\displaystyle L = \lim_{\text{x}\to 1^(+)} \frac{-1}{\text{x}+1}\\\\\\\displaystyle L = (-1)/(1+1)\\\\\\\displaystyle L = -(1)/(2)\\\\\\`

In the second step, I used the difference of squares rule to factor.

The (x-1) terms cancel which allows us to plug in x = 1. We plug this value in because x is approaching 1 from the right side.