To find this limit, we can use L’Hôpital’s rule, which states that if we have an indeterminate form, such as 0/0 or infinity/infinity, we can differentiate the numerator and denominator separately and take the limit again.
Applying L’Hôpital’s rule yields:
lim as x->0 of sinx/x
= lim as x->0 of cosx/1
= cos(0)/1 (since 0 is the limit of x as x approaches 0)
= 1
Therefore, the limit of sinx/x as x approaches 0 is equal to 1.
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