lim x->0 sinx/x
1
To evaluate this limit, we can use one of the fundamental limits of calculus, which says that:
lim x->0 sinx/x = 1
To prove this limit, we can use L’Hopital’s rule:
lim x->0 sinx/x = lim x->0 cosx/1 = cos0/1 = 1
Therefore, the limit of sinx/x as x approaches 0 is 1. This means that as x gets closer and closer to 0 (from both the left and the right), the ratio of sinx to x approaches 1. This limit is important in calculus and in other areas of mathematical analysis, as it shows that sinx and x are intimately related near 0.
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