lim -> 0 sin(2x) /(x*cos(x) ) help

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lim -> 0 sin(2x) /(x*cos(x) ) help

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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sin (2x) = 2sin(x)cos(x) so sin(2x) /(x*cos(x) =2sin(x)cos(x)/x*cos(x)=2sinx/x which as x->0 goes to 1
no, answer is 2
ups sry, forgot about 2 multuplying: lim 2sinx/x=2*1=2 x->0

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Other answers:

don't undestand you
sin (2x) can be written like: sin (2x) = 2sin(x)cos(x) substituting this expretion in the original one: sin(2x) /(x*cos(x) =2sin(x)cos(x)/x*cos(x)=2sinx/x taking limits, and noticing that lim as x->0 of sinx/x=1: lim 2sinx/x=2*1=2 x->0
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no
why not? l'Hôpital rule
yes, using l'hospital's rule works
Don't break your head ! You know that sin(x)=x as x tends to zero. So sin(2x) = 2x. In the denominator, keep x as it is and cos(x)=1. Hence the answer
thanks, but the image is ok?
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claro que es posible es solamente derivar arriba y abajo como lo muestras en la imagen y ya

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