When we look at the function cot(x), which represents the ratio of the cosine of x divided by the sine of x, we find that as x approaches certain values, the function becomes larger and larger without bound. This means that the value of cot(x) keeps getting bigger and bigger, either becoming infinitely large in the positive direction (positive infinity, ∞) or infinitely large in the negative direction (negative infinity, -∞). Therefore, we say that the limit of cot(x) does not exist, or we can express it as lim cot(x) = DNE.