Final answer:
To find all values for the constant 'k' such that the limit exists, we must analyze the function and ensure that including 'k' results in a finite limit. It is not sufficient to arbitrarily assign 'k' to any real number or to infinity. The correct option is B) By taking the limit of the expression and ensuring it is a finite value.
Step-by-step explanation:
The question asks how we can find all values for the constant 'k' such that the limit of an expression exists. To determine these values, one must not just assign any real number to k, nor can k be set to infinity as a default value. Instead, we should carefully examine the behavior of the function as we approach a particular point to ensure that the limit is a finite value.
If the limit exists, then the function should approach a specific value as the input approaches a particular point. If including the constant k in the function allows for a finite limit, then k works within the context of the limit. If our calculations or analysis of the function show that k can be any real number and still result in a finite limit, then we can say that the limit exists for all real values of k. However, if the existence of the limit depends on the value of k, then we must determine the specific values of k that make the limit finite.
Based on the information provided and the question, we ascertain that the correct option is B) By taking the limit of the expression and ensuring it is a finite value. This requires analyzing the given function and determining the conditions under which the limit is well-defined and finite.