limit as x approaches 0: sinx/x
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To find the limit as x approaches 0 of sinx/x, we can use L’Hopital’s Rule, which states that if we have an indeterminate form of 0/0 or infinity/infinity, we can take the derivative of the numerator and denominator and try to evaluate the limit again.
Taking the derivative of sinx with respect to x, we get cosx. Taking the derivative of x with respect to x, we get 1. Therefore, we have:
limit as x approaches 0: sinx/x = limit as x approaches 0: cosx/1
Now, we can directly evaluate this limit, since cos(0) = 1. Therefore, the answer is:
limit as x approaches 0: sinx/x = 1
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