Asked by Francis
lim x->0 (Sin^3 3x - 3x^3)/(x^3) (x^4)
Answers
Answered by
Steve
The left term can be seen as
(sin3x/x)^3 - 3
= 27(sin3x/3x)^3 - 3
now, we all know that lim sinu/u = 1 as u->0, so the limit of all that is just
27-3 = 24
multiply that by x^4 and you just wind up with 0 as x->0
Still not sure what that x^4 is doing in there. It just clutters up the concept of the 0/0 limit on the left.
(sin3x/x)^3 - 3
= 27(sin3x/3x)^3 - 3
now, we all know that lim sinu/u = 1 as u->0, so the limit of all that is just
27-3 = 24
multiply that by x^4 and you just wind up with 0 as x->0
Still not sure what that x^4 is doing in there. It just clutters up the concept of the 0/0 limit on the left.
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