If `f(x)=|x-1|-[x]`, where `[x]` is the greatest integer less than or equal to x, then

Question

If `f(x)=|x-1|-[x]`, where `[x]` is the greatest integer less than or equal to x, then

If `f(x)=|x-1|-[x]`, where `[x]` is the greatest integer less than or equal to x, then
A. `underset(xto0)lim[f(x)]=0`
B. `underset(xto0)lim[f(x)]=1`
C. `underset(xto0)lim[(f(x))/(x)]` does not exist
D. `underset(xto0)lim[(f(x))/(x)]` exists

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - A::D
`f(1+0)=underset(hto0)lim(|1+h-1|-[1+h])=underset(hto0)lim(h-1)=-1`
`f(1-0)=underset(hto0)lim(|1-h-1|-[1-h])=underset(hto0)lim(h-0)=0`

5 views Answered 2023-02-05 15:29