Question

Suppose lim g(x) = 3, lim f(x) = 1, lim h(x) = 0. What can be said about the limits of the functions g(x), f(x), and h(x)?

1) The limit of g(x) is 3, the limit of f(x) is 1, and the limit of h(x) is 0.
2) The limit of g(x) is 1, the limit of f(x) is 3, and the limit of h(x) is 0.
3) The limit of g(x) is 0, the limit of f(x) is 1, and the limit of h(x) is 3.
4) The limit of g(x) is 0, the limit of f(x) is 3, and the limit of h(x) is 1.

Answer 1

The correct statement about the limits of the functions g(x), f(x), and h(x) given that lim g(x) = 3, lim f(x) = 1, and lim h(x) = 0 is: The limit of g(x) is 3, the limit of f(x) is 1, and the limit of h(x) is 0.

Step-by-step explanation:

If we are given that lim g(x) = 3, lim f(x) = 1, and lim h(x) = 0, this information tells us the behavior of the functions g(x), f(x), and h(x) as x approaches a certain value. In the context of limits, the value that x is approaching is not given, but whatever value that may be, g(x) approaches 3, f(x) approaches 1, and h(x) approaches 0 as x approaches that particular value. Based on these limit values, the correct statement about the limits of these functions is option 1), which correctly restates the given information: The limit of g(x) is 3, the limit of f(x) is 1, and the limit of h(x) is 0.