Question

If $f\left(x\right)=\frac{\tan x}{\tan x}$ then

• A. $\underset{x\to 0}{lim}f\left(x\right)$ does not exists
• B. $\underset{x\to 0}{lim}f\left(x\right)$ exists
• C. $f\left(x\right)$ has fundamental period $\pi$
• D. all of these

Answer 1

Answer: (B)

$\underset{x\to 0}{lim}f\left(x\right)$ exists

$f\left(x\right)=\frac{\tan x}{\tan x}$

$\underset{x\to 0}{lim}\frac{\tan x}{x}\times \frac{x}{\tan x}=1\times 1=1$

$\therefore$Limit exists.