Let denote an angle measured in degrees and define .

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let α\alpha denote an angle measured in degrees and define f(α)=sin⁡ααf(\alpha)=\dfrac{\sin \alpha}{\alpha}. (a) Evaluate lim⁡α→0f(α)\displaystyle\lim_{\alpha\to 0} f(\alpha), clearly indicating how you convert between degree and radian measure in your calculation. (b) Explain why the limit in part (a) differs from lim⁡x→0sin⁡xx\displaystyle\lim_{x\to 0} \dfrac{\sin x}{x} when xx is measured in radians. Discuss the implications of this difference for the use of trigonometric limits in calculus and for the small-angle approximations common in physics and engineering.

Related theory

Browse the problem library