lim theta->0 sin(theta) / theta = ___________________
1
The limit as theta approaches 0 of sin(theta)/theta is equal to 1.
To prove this, we can use L’Hopital’s rule:
lim theta->0 sin(theta) / theta = lim theta->0 cos(theta) / 1 = cos(0) / 1 = 1
Alternatively, we could use the squeeze theorem. Since the sine function is bounded between -1 and 1, we can say:
-1 <= sin(theta)/theta <= 1 Then, taking the limit as theta approaches 0, the squeeze theorem tells us that: lim theta->0 sin(theta) / theta = 1
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