Question

If $f\left(x\right)=\frac{3x+{\tan }^{2}x}{x}$ is continuous at $x=0$, then $f\left(0\right)$ is equal to:

• A. $3$
• B. $2$
• C. $4$
• D. $0$

Answer 1

The correct option is A $3$

Given,

$f\left(x\right)=\frac{3x+{\tan }^{2}x}{x}$ is continous at $x=0$

$\therefore f\left(0\right)=\underset{x\to 0}{lim}\frac{3x+{\tan }^{2}x}{x}$

$=\underset{x\to 0}{lim}(3+\frac{{\tan }^{2}x}{x^2}\cdot x)$

$=3+1^2\cdot 0=3$