Question

$\underset{x\to 0}{\lim }\left[\frac{a\sin x}{x}\right]+\left[\frac{b\tan x}{x}\right]$, where $a,b$ are integers and [] denotes integral part, is equal to

• A. $a+b$
• B. $a+b-1$
• C. $a-b$
• D. $a-b-1$

Answer 1

Answer: (B)

$\underset{x\to 0}{\lim }\left[\frac{a\sin x}{x}\right]+\left[\frac{b\tan x}{x}\right]$
$[\text{as}x\to 0,\frac{\sin x}{x}\to 1$ but $\frac{\sin x}{x}<1$ while $\frac{\tan x}{x}\to 1$ but $\frac{\tan x}{x}>1]$
$=(a-1)+b$
$=a+b-1$