Final answer:
The limit of the function e^(1/x) as x approaches infinity is 1, because 1/x approaches 0 and e^0 is equal to 1.
Step-by-step explanation:
The student is asking about the behavior of the function e^(1/x) as x approaches infinity. This involves the concept of limits, which is a fundamental topic in calculus. To evaluate the limit of e^(1/x) as x approaches infinity, we consider what happens to 1/x as x becomes very large.
As x grows, 1/x gets smaller and approaches 0. Since the exponential function e^y approaches 1 as y approaches 0, the limit of e^(1/x) as x approaches infinity is 1. Therefore, the correct answer is B. 1.
To evaluate the limit of e^(1/x) as x approaches infinity, we can use the properties of exponential functions. As x approaches infinity, the value of 1/x approaches 0. Therefore, raising e to the power of 1/x will become e^0, which is equal to 1. So, the limit of e^(1/x) as x approaches infinity is 1. The correct answer is B.