Evaluate the limits. lim _(xarrow 6^-)(x-6)/(vert x-4vert )= lim _(xarrow 6^+)(x-6)/(vert x-4vert )= Does lim _(xarrow 6)(x-6)/(vert x-4vert ) exist?

To evaluate the given limits, we need to consider the behavior of the function as approaches from both the left and the right.1. When approaches from the left, the numerator is negative, and the denominator is positive. Therefore, the fraction is negative.As gets closer to , the numerator approaches , and the denominator approaches . So, the limit is: 2. When approaches from the right, the numerator is positive, and the denominator is positive. Therefore, the fraction is positive.As gets closer to , the numerator approaches , and the denominator approaches . So, the limit is: 3. Does exist?For the limit to exist, the left-hand limit and the right-hand limit must be equal. However, we have: Since the left-hand limit and the right-hand limit are not equal, the limit does not exist.