Question

The value $\underset{\theta \to 0}{\lim }\frac{\tan \left(\theta \right)}{\theta }$ is

• A. -1
• B. 0.0
• C. 1
• D. 2

Answer 1

The correct option is C 1

$\underset{\theta \to 0}{\lim }\frac{\tan \left(\theta \right)}{\theta }=\underset{\theta \to 0}{\lim }\frac{1}{\cos \left(\theta \right)}\frac{\sin \left(\theta \right)}{\theta }$

$=\frac{1}{\cos \left(0\right)}\underset{\theta \to 0}{\lim }\frac{\sin \left(\theta \right)}{\theta }$

$\frac{1}{1}\left(1\right)=1$

Hence, $\underset{\theta \to 0}{\lim }\frac{\tan \left(\theta \right)}{\theta }=1$