When x tends to zero, what is the limit of the square of 1 / x minus the square of Cotx

When x tends to zero, what is the limit of the square of 1 / x minus the square of Cotx

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What is the limit of (1 + x) ^ Cotx when x tends to zero?
When x tends to 0, what is the limit of (1 + x) ^ Cotx

(1 + x) ^ Cotx = (1 + x) ^ ((cosx) ^ 2 / (SiNx) ^ 2), when x tends to 0, SiNx = x (Infinitesimal Substitution of the same order), let t = x ^ 2, then t also tends to 0, (cosx) ^ 2 tends to 1, so LIM (1 + x) ^ Cotx = LIM (1 + T) ^ (1 / T) = e, (x tends to 0, t tends to 0)

LIM (1 + 3tan ^ 2 x) ^ cot2x x tends to 0
Let's find the limit
I copied the wrong title, but I got the original one

lim(1+3tan^2x)^cot2x
=lim(1+3tan^2x)^(3tan^2x/3tan^2x * cot2x)
=lim{(1+3tan^2x)^[1/(3tan^2x)]}^(cot2x * 3tan^2x)
=lim e^(cot2x * 3tan^2x)
=lim e^(3tan2x)
=lim e^0
=1