Question

${lim}_{\theta \to 0}\frac{sinm\theta }{\theta }$ , where m is an integer, is one of the following:

• A. m
• B. $m\pi$
• C. m$\theta$
• D. 1

Answer 1

The correct option is A m

${lim}_{\theta \to 0}\frac{sinm\theta }{\theta }\left(\frac{0}{0}\right)$

Apply L'Hospital's Rule

${lim}_{\theta \to 0}\frac{mcosm\theta }{1}=m$

Alternative Solution:

${lim}_{\theta \to 0}\frac{sinm\theta }{\theta }={lim}_{\theta \to 0}m\frac{sinm\theta }{m\theta }=m\left(1\right)=m$