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Question
limit as x approaches 0(e^x-sinx/x-sinx)
If you remember from elementary mathematices, powers are done first,
then division, and then the subtraction. The problem would appear
to be lim(x->0)(e^x - sinx/x - sinx). If this is the problem,
we know e^0 is 1, sinx/x goes to 1, and sin(0) is 0.
The answer, if this were the case, would be 1 - 1 - 0 = 0.
However, I'm not sure that that is correct.
If the problem were e^((x-sin)/(x-sinx)), then it could be said to
be e^1 = e since (x-sinx)/(x-sinx) reduces to 1. It is only undefined when x=sinx (at x=0), but the limit is still 1.
Now for a third case, the problem might be e^(x-sinx) / (x-sinx).
In this case, the numerator goes to e^0 = 1 and the
denominator goes to 0, so the function is undefined.
If one of these three choices were not the case, I wait to hear
back from you with an explanation of how the problem looks
with the appropriate parenthesis in there. By the way, sinx should really be sin(x), but I believe that we can understand that one, so
it's OK to leave it as sinx.
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