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I need to to find this limit:

lim (x*sin(x))

x->0 (2(1-cos(x))

After applying l'Hopital's rule twice I get the answer 1.

However, when I ask Maple 11 to find the limit it returns 0 as the answer. I went to a bit farther and made Maple 11 apply l'Hopital's twice as well and it also came up with the answer being 1. In fact, after only one application of l'Hopital's rule, Maple returned 1 as the answer. My only conclusions are that either I don't fully understand the subtleties of l'Hopital's rule or that Maple is wrong.

First application of l'Hopital's rule gives:

lim (sin(x)+x*cos(x))

x->0 (2*sin(x))

Second application:

lim (2*cos(x)-x*sin(x))

x->0 (2*cos(x))

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# Simple limit giving me trouble

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