Discovering The Limit Of Sin(Theta)/Theta Approaching 0 Using L’Hopital’S Rule

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

1

The limit of sin(theta)/theta as theta approaches 0 is 1.

One way to determine this is by using L’Hopital’s rule. We can rewrite the expression as:

lim theta->0 sin(theta) / theta = lim theta->0 (d/dtheta sin(theta)) / (d/dtheta theta)

Since the derivative of sin(theta) with respect to theta is cos(theta), and the derivative of theta with respect to theta is 1, we can apply L’Hopital’s rule to get:

lim theta->0 sin(theta) / theta = lim theta->0 cos(theta) / 1

Evaluating this limit as theta approaches 0 gives us:

lim theta->0 sin(theta) / theta = cos(0) / 1 = 1

Therefore, we can conclude that the limit of sin(theta)/theta as theta approaches 0 is 1.

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