Calculate the following limit: lim -x/tan(3x) as x approches to 0

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question to comply with the same.

We have to find the value
of lim x--> 0 [ -x/tan(3x)]

If we substitute x = 0,
we get the indeterminate form 0/0. This allows the use of l'Hopital's rule. We
substitute the numerator and denominator by their
limits.

lim x--> 0 [
-x/tan(3x)]

=> lim x--> 0[ -1/3*(sec
3x)^2]

substitute x =
0

=>
-1/3

The required limit is
-1/3