lim(1-cos(x)/x)x->0
0
To evaluate the limit:
lim(1-cos(x)/x) as x approaches 0
We can solve it using L’Hopital’s rule, which states that if the limit of a function f(x) as x approaches a particular value is indeterminate (such as 0/0), and the limit of the derivative of f(x) as x approaches the same value exists, then the limit of f(x) as x approaches that same value equals the limit of the derivative of f(x) as x approaches that same value.
Using L’Hopital’s rule:
lim(1-cos(x)/x) = lim(sin(x)/1) as x approaches 0
= sin(0)/1
= 0/1
= 0
Therefore,
lim(1-cos(x)/x) as x approaches 0 is equal to 0.
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