lim⁡𝑥→0cos⁡(𝑥)−𝑥x→0lim​ cos(x)−x =

The limit you're asking about seems to be incorrectly written. It should be in the form of "lim (f(x) - g(x)) / h(x) as x approaches a certain value".

If you're asking for the limit of (cos(x) - 1)/x as x approaches 0, then the solution would be 0. This is because cos(0) is 1, so the numerator becomes 0, and any number divided by itself is 0.

If you're asking for the limit of (cos(x) - x)/x as x approaches 0, then the limit does not exist. This is because the numerator does not approach a specific value as x approaches 0.

Please clarify the question if it's different from these two cases.