Let `lim_(x->0)([x]^2)/(x^2)=l and lim_(x->0)([x^2])/(x^2)=m ,` where `[dot]` denotes greatest integer. Then (a)`l` exists but `m` does not (b)`m` exists but `l` does not (c)both l and m exist (d) neither l nor m` exists

Options

A. `-(1)/(sqrt(2))`
B. `(1)/(sqrt(2))`
C. `sqrt(2)`
D. `-sqrt(2)`

Answer

B

Explanation

`([x]^(2))/(x^(2))=[{:(0", ""if "0ltxlt1),((1)/(x^(2))","" if "-1ltxlt0):}impliesl " does not exist"`
`([x]^(2))/(x^(2))=[{:(0", ""if "0ltxlt1),(0","" if "-1ltxlt0):}impliesm" exists and is equal to 0"`