Final answer:
If f(x) is always greater than 1 and the limit of f(x) as x approaches 0 exists, then the limit of f(x) as x approaches 0 is also greater than 1.
Step-by-step explanation:
The student is asking about the limit of a function f(x) as x approaches 0. They already know that f(x) is always greater than 1. The question is whether the limit of f(x) as x approaches 0 is also greater than 1.
Since f(x) is greater than 1 for all x, it means that as x gets closer and closer to 0, f(x) also gets closer and closer to a value greater than 1. Therefore, the limit of f(x) as x approaches 0 is indeed greater than 1.
Example: If we have a function f(x) = 2 + x, for all values of x greater than 0, f(x) will be greater than 1. And as x approaches 0, f(x) will approach 2, which is greater than 1.