lim⁡𝑥→0(cos 𝑥𝑥)=x→0lim​ ( xcos x​ )=

The limit of the function as x approaches 0 is undefined because the function is in the form of 0/0 which is an indeterminate form. However, we can use L'Hopital's Rule to find the limit. L'Hopital's Rule states that the limit of a quotient of two functions as x approaches a certain value is equal to the limit of the quotients of their derivatives.

Step 1: Differentiate the numerator and the denominator separately. The derivative of cos(x) with respect to x is -sin(x). The derivative of x with respect to x is 1.

Step 2: Apply L'Hopital's Rule. lim x→0 (cos x / x) = lim x→0 ((-sin x) / 1)

Step 3: Evaluate the limit. As x approaches 0, -sin(x) approaches 0. Therefore, the limit of the function as x approaches 0 is 0.