Question

Use limit properties to evaluate $\underset{x\to 4}{lim}\frac{3x^2\tan \frac{\pi }{x}}{x}$

• A. $12$
• B. $14$
• C. $16$
• D. $18$

Answer 1

The correct option is A $12$

$\underset{x\to 4}{lim}\frac{3x^2\tan \frac{\pi }{x}}{x}=\underset{x\to 4}{lim}\left(3x\tan \frac{\pi }{x}\right)$, simplify

$=3\left(4\right)\tan \frac{\pi }{4}=12\left(1\right)=12$, [substitute the limit ]

The from of the limit is not indeterminate, so we can substitute the limit value