Final answer:
If the limit of f(x) is 1 and the limit of g(x) is 0, the limit of f(x) g(x) does not exist.
Step-by-step explanation:
The statement "lim x→5 f(x) = 1 and lim x→5 g(x) = 0" tells us that the limit of f(x) as x approaches 5 is 1 and the limit of g(x) as x approaches 5 is 0. In the expression lim x→5 f(x) g(x), we are multiplying f(x) and g(x) together. If one of the limits is 0, then when we multiply it by f(x), the product will also be 0. But in this case, the limit of f(x) is 1, which means the product will not be 0. Therefore, the limit lim x→5 f(x) g(x) does not exist.