The value of the limit of the function given when the value of x tends to zero is 0
The limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular inputs.
Given the function limit below;
lim x→0 [1 − cos(2x) /x]
Substitute the value of x into the expression to have;
f(0) = 1-cos2(0)/0
f(0) = 1-1/0
f(0) = 0/0 (ind)
Apply the L'hospital rule to have:
lim x→0 [ − (-2sin2x)) /1]
Substitute the value of x into the result
f(0) = 2sin2(0)/1
f(0) = 2(0)
f(0) = 0
Hence the value of the limit of the function given when the value of x tends to zero is 0
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