Question

Let $f\left(x\right)=\{\begin{array}{cc}\frac{3x+4\tan x}{x}& forx\ne 0\\ 7& forx=0\end{array}$ then $f\left(x\right)$ is

• A. continuous at $x=0$
• B. not continuous at $x=0$
• C. not determined at $x=0$
• D. $L{t}_{x\to 0}f\left(x\right)=8$

Answer 1

The correct option is A continuous at $x=0$

$\underset{x\to 0}{lim}\frac{3x+4\tan x}{x}$

$=3+4.{lim}_{x\to 0}\frac{\tan x}{x}$

$=3+4=7=f\left(0\right)$
Hence $f\left(x\right)$ is continuous at $x=0$.