Calculate the following limit: lim -x/tan(3x) as x approches to 0
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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
The required limit is -1/3