Final answer:
The limit expression simplifies to 0 as all terms cancel out when x is substituted with e, thus the correct option is A. 0.
Step-by-step explanation:
The question asks us to evaluate the limit as x approaches e of the expression (e20 - 3x) / (e20 - 3e). Initially, this may look like a complex limit problem, but it simplifies to a much easier task. Let's break it down:
The constant e20 appears both in the numerator and the denominator, thus they cancel each other out. Similarly, 3e will cancel out the -3x when x is substituted with e. After substitution, all terms cancel out, leaving the expression to be evaluated as 0/0, which is an indeterminate form, often a signal to apply L'Hôpital's Rule. However, in this case, after the constants cancel out, we can directly see that the numerator becomes zero irrespective of the other terms since x=e negates the term -3x with 3e. No further calculations are necessary to conclude that the answer is 0. Hence, the correct option is A. 0.