lim theta->0 sin(theta) / theta = ___________________
The limit of sin(theta) / theta as theta approaches 0 can be found using L’Hôpital’s Rule
The limit of sin(theta) / theta as theta approaches 0 can be found using L’Hôpital’s Rule. Before we apply this rule, let’s rewrite the expression as:
lim theta->0 sin(theta) / theta = lim theta->0 (1 / (1 / sin(theta / theta)))
Now, let’s differentiate the numerator and denominator separately with respect to theta:
d/dtheta (sin(theta)) = cos(theta)
d/dtheta (theta) = 1
Now we can apply L’Hôpital’s Rule:
lim theta->0 sin(theta) / theta = lim theta->0 (cos(theta) / 1)
Since cosine of 0 is equal to 1:
lim theta->0 sin(theta) / theta = 1
Therefore, the limit of sin(theta) / theta as theta approaches 0 is equal to 1.
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