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Calculus Level 2

$\large \displaystyle \lim_{x\rightarrow 0} \frac{\sin (x^{\circ}) }{x} = \ ?$

Note: $x^\circ$ shows that $x$ is measured in degrees.

\frac{\pi}{180}

\frac{180}\pi

1 solution

Vishwak Srinivasan
Jul 26, 2015

$\left(\dfrac{180}{\pi}\right)^{\circ} = 1rad$

$\Rightarrow x^{\circ} = \dfrac{\pi x}{180}$

$L = \displaystyle \lim_{x \to 0} \dfrac{\sin x^{\circ}}{x}$

$\Rightarrow L = \displaystyle \lim_{x \to 0} \dfrac{\sin \frac{\pi x}{180}}{\frac{\pi x}{180}} \dfrac{\pi}{180} = \boxed{\dfrac{\pi}{180}}$

Shouldn't the answer be pi/180

Kamal Hisyam - 5 years, 10 months ago

Thanks for identifying the typo. Yes, the answer should be $\dfrac{\pi}{180}$ .

Vishwak Srinivasan - 5 years, 10 months ago