Question

$\underset{x\to 0}{\lim }\frac{\sin x^0}{x}$ is equal to

(a) 1
(b) π
(c) x
(d) π/180

Answer 1

(d) $\frac{\mathrm{\pi }}{180}$

$$\begin{gathered} \underset{x\to 0}{\lim }\frac{\sin x^0}{x} \\ =\underset{x\to 0}{\lim }\frac{\sin {\displaystyle \frac{\mathrm{\pi }}{180}}x}{x} \\ =\underset{x\to 0}{\lim }\frac{\sin \left({\displaystyle \frac{\mathrm{\pi }}{180}}x\right)}{\left({\displaystyle \frac{\mathrm{\pi }}{180}}x\right)}\times \frac{\mathrm{\pi }}{180} \\ =\frac{\mathrm{\pi }}{180}\times 1=\frac{\mathrm{\pi }}{180} \end{gathered}$$