Question

$\displaystyle\lim _{x \rightarrow 0}\left[\frac{a \sin x}{x}\right]+\left[\frac{b \tan x}{x}\right]$, 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)

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