`lim(x->a_-) {(|x|^3)/a-[x/a]^3} ,(a < 0)`, where `[x]` denotes the greatest integer less than or equal to `x` is equal to:

Options

A. (a) `a^2-2`
B. (b) `a^2-1`
C. (c) `a^2`
D. (d) `a^2+1`

Answer

C

Explanation

`because` For a-1 < x < a , `[x/a]=0 " " therefore lim_(x to a^-) ((|x|^3)/a-[x/a]^3)=lim_(x to a^-)((|x|^3)/a-0)=lim_(h to 0) ((|a-h|^3)/a)=a^3/a=a^2`