lim theta->0 sin(theta) / theta = ___________________
1
The limit as theta approaches 0 of sin(theta) / theta is equal to 1.
To see why, we can use the squeeze theorem. We know that sin(theta) is always between -1 and 1, inclusive. Therefore, we can write:
-1 <= sin(theta) / theta <= 1 Now, as theta approaches 0, both the numerator and denominator approach 0 as well. Using the squeeze theorem, we can conclude that the limit of sin(theta) / theta as theta approaches 0 must also be 1. Alternatively, we can use L'Hopital's rule. Taking the derivative of both the numerator and denominator with respect to theta, we get: lim theta->0 sin(theta) / theta = lim theta->0 cos(theta) / 1 = 1
since the derivative of sin(theta) is cos(theta) and the derivative of theta is 1.
More Answers:
[next_post_link]