Question

What is \(\mathop {\lim }\limits_{\theta \to 0} \frac{{\sin \theta }}{\theta }\) equal to?
1. θ
2. Sinθ
3. 0
4. 1

Answer 1

Correct Answer - Option 4 : 1

Concept:

\(y=\mathop {\lim }\limits_{\theta \to 0} \frac{{\sin \theta }}{\theta }\)

It gives \(\frac{0}{0}\) form

Therefore, by applying L’ Hospital's rule....(differentiate both numerator and denominator)

We will get

\(y=\mathop {\lim }\limits_{\theta \to 0} \frac{{\cos \theta }}{1}=\frac{cos~0}{1}=\frac{1}{1}=1\)