lim theta->0 1 – cos(theta) / theta = ___________________
0
To evaluate the limit:
lim theta->0 (1 – cos(theta)) / theta
We can use L’Hopital’s rule which states that if the limit of f(x) / g(x) as x approaches a limit L yields the indeterminate form 0 / 0 or infinity / infinity, then the limit of f(x) / g(x) as x approaches L is equal to the limit of the derivative of f(x) divided by the derivative of g(x) as x approaches L, provided that the limit of the derivative of g(x) as x approaches L is non-zero.
So applying L’Hopital’s rule to the above limit, we get:
lim theta->0 (1 – cos(theta)) / theta
= lim theta->0 sin(theta) / 1
=0/1=0
Therefore, the limit of (1 – cos(theta)) / theta as theta approaches 0 is equal to 0.
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