Discovering the Limit of (1-cos(θ))/θ using L’Hospital’s Rule | Math Optimization

lim theta->0 1 – cos(theta) / theta = ___________________

0

To find the limit of the given expression as theta approaches 0, we can use L’Hospital’s rule.

First, let’s simplify the expression:

(1 – cos(theta)) / theta

= (1/theta) – (cos(theta)/theta)

Now, taking the limit as theta approaches 0, we get:

lim theta->0 (1/theta) – (cos(theta)/theta)

We can’t directly substitute 0 for theta, as it would result in division by zero, so we need to use L’Hospital’s rule.

Differentiating both the numerator and denominator with respect to theta, we get:

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

= 0

Therefore, the limit as theta approaches 0 of (1 – cos(theta)) / theta is 0.

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