Final answer:
The limit of the function lim x->3 (2 - (5/(x-3)^2)) is -infinity as the denominator (x-3)^2 approaches zero and the fraction 5/(x-3)^2 grows without bound.
Step-by-step explanation:
The student's question is regarding the evaluation of a limit in mathematics. Specifically, the limit in question is lim x->3 (2 - (5/(x-3)^2)). To find this limit as x approaches 3, we have to consider the behavior of the denominator (x-3)^2 as x approaches 3. When x is very close to 3, the value of (x-3)^2 becomes very small. As a result, the value of 5/(x-3)^2 becomes very large, because dividing by an increasingly smaller number results in a larger and larger result. As the value of x gets closer to 3 from either side, the fraction 5/(x-3)^2 approaches positive infinity, and hence the entire expression approaches -infinity because we are subtracting this fraction from 2. Therefore, the correct answer to the limit of the function as x approaches 3 is option a) -infinity.