lim theta->0 1 – cos(theta) / theta = ___________________
0
To solve this limit, we can first notice that we have a 0/0 indeterminate form in the expression. Therefore, we can use L’Hopital’s rule to evaluate the limit.
Taking the derivative of the numerator and denominator separately, we get:
lim theta->0 (sin(theta)) / 1
Since sin(0) = 0, the limit evaluates to:
lim theta->0 (1 – cos(theta)) / theta = 1
Therefore, the answer is 1.
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