To evaluate the limit as x approaches 0 for sinx/x, we need to apply L’Hopital’s rule, as we have an indeterminate form of 0/0. Here’s how we can proceed:
lim x → 0 sin x / x
= lim x → 0 (d/dx sin x) / (d/dx x) (Applying L’Hopital’s rule)
= lim x → 0 cos x / 1
= cos 0 / 1 (Substituting x = 0, as no longer it’s an indeterminate form)
= 1
Therefore, the limit of sinx/x as x approaches 0 is equal to 1.
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