By definition, hyperbolic cotangent `coth(x)` is equal to `(cosh(x))/(sinh(x)),` which is equal to `(e^x + e^(-x))/(e^x - e^(-x)).`
When `x -> 0^-,` both `e^x` and `e^(-x)` tend to `1.` But while `e^x -> 1^-,` `e^(-x) = 1/e^x -> 1+.` Therefore the numerator tends to `1 + 1 = 2,` and the denominator tends to `1^(-) - 1^+ = 0^-.`
And finally `2/0^-` gives the limit of `-oo.` This is the answer.
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