Final answer:
To calculate lim (x → 2) cot(x), take the reciprocal of tan(2). Since tan(2) has a specific numeric value, cot(2) also has a specific value that can be determined using a calculator, hence the limit exists and is the cotangent of 2 radians.
Step-by-step explanation:
The student is asking for the limit of the cotangent function as x approaches 2. To find lim (x → 2) cot(x), we must first recognize that cot(x) is the reciprocal of tan(x), which means that cot(x) = 1/tan(x). As x approaches 2, tan(2) approaches a specific numeric value, and therefore, cot(2) also approaches a specific numeric value, which is the reciprocal of tan(2).
The trigonometric limit can be calculated directly by substituting x with 2 in the cotangent function if no indeterminate forms are present. Evaluating tan(2) and taking the reciprocal of that value will give us the limit of cot(x) as x approaches 2. The value of tan(2) can be found using a calculator or trigonometric tables since it is not one of the special angles where the tangent (or cotangent) value is known exactly. Thus, lim (x → 2) cot(x) exists and is equal to the cotangent of 2 radians.