Question

If $a>0,{lim}_{x\to \infty }\frac{[ax+b]}{x}$ is where $[.]$ denotes G.I.F.

• A. $0$
• B. $1$
• C. $\left[a\right]$
• D. $\left[b\right]$

Answer 1

The correct option is C $\left[a\right]$

$\underset{x\to \infty }{lim}\frac{[ax+b]}{x}$

$=\underset{x\to \infty }{lim}\frac{x[a+b/x]}{x}$

$=\left[a\right]$

if $a$ is integer,

$\left[a\right]=a$

if $a$ is rational no.

$\left[a\right]=a-\left\{a\right\}$

$\therefore$ Ans = $\left[C\right]$.