Math Explained: Calculating The Limit Of Sin(Theta)/Theta As Theta Approaches 0.

lim theta->0 sin(theta) / theta = ___________________

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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.

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