Limit of theta –>0 of 1-cos(0)/0 = ?
0
To compute the limit of theta approaching 0 of (1-cos(theta))/theta, we can apply L’Hopital’s rule, which states that if we have an indeterminate form of the type 0/0 or infinity/infinity, we can take the derivative of the numerator and denominator with respect to the variable approaching the limit and compute the limit of the resulting expression.
Applying this rule, we get:
lim theta –> 0 (1-cos(theta))/theta
= lim theta –> 0 sin(theta)/1
= sin(0)/1
= 0/1
= 0
Therefore, the limit of theta approaching 0 of (1-cos(theta))/theta is 0.
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