SOLUTION: Limit x approaches 0 sin2x/x

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Question 807777: Limit x approaches 0 sin2x/x
Answer by fcabanski(1391) About Me  (Show Source):
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Limit as x approaches 0 of sin(nx)/x = n. So, limit as x approaches 0 of sin(2x)/x = 2.


One way to prove it is with L'Hospital's Rule. It states that if a limit is indeterminate via substitution, such as sin(0)/0 = 0/0 in this case, then the limit as x approaches a of f(x)/g(x) = limit x approaches a f'(x)/g'(x) (the limit of the ratio of the derivatives.) Derivative of sin(2x) is 2cos(2x) and derivative of x = 1.


Limit as x approaches 0 of 2cos(2*0)/1 = 2*cos(0)/1 = 2*1/1 = 2.