What is the value of `lim_(xto1) ((x-1)^(2))/(|x-1|)` ?

Options

A. 0
B. 1
C. -1
D. The limit does not exist

Answer

A

Explanation

Let `f(x)=((x-1)^(2))/(|x-|)={{:((x-1)",",xge1),(-(x-1)",",xlt1):}`
Now, `LHL=underset(hto0)limf(1-h)`
`=underset(hto0)lim[-(-h-1)]=underset(hto0)limh=0`
`andRHLunderset(hto0)limf(1+h)`
`=underset(hto0)lim(1+h-1)=underset(hto0)h=0`
`:.LHL=RHL`
`:.underset(xto0)limf(x)=LHL=RHL`
`impliesunderset(xto0)lim((x-1)^(2))/(|x-1|)=0`