Question

Let `lim_(xto0) ([x]^(2))/(x^(2))=m,` where `[.]` denotes greatest integer. Then,
A. `-(1)/(sqrt(2))`
B. `(1)/(sqrt(2))`
C. `sqrt(2)`
D. `-sqrt(2)`

Answer 1

Correct Answer - B
`([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"`