Please answer and explain which of the follow are true for the given limit.
Selecting Option E ONLY is marked incorrect.
Selecting Options A, B & E is marked incorrect.
What is the answer :(
Options A & E are the answers to this given question. Thanks to everyone for their contributions.
- TomVLv 710 months ago
E is a true statement. If the function is continuous as x becomes very large, it may or may not have a horizontal asymptote at y = 2, but since nothing is known about the function other than its limit as x → ∞, you cannot say with certainty that the function is asymptotic to y = 2. Consider the function f(x) = 2. The limit as x approaches infinity is 2, but the function does not have a horizontal asymptote at y = 2.
B is a true statement. Since x = ∞ is not in the domain of the function, the only way that lim(x→∞) f(x) can exist is if the function is continuous as x approaches ∞.
The other statements may of may not be true, but lim(x→∞) f(x) = 2 does not require that any of them MUST be true.
- 10 months ago
A might not be true, simply because we know that y = 2 fits the bill and a line can't be its own asymptote, unless I'm completely wrong about that.
B is true.
C is definitely not true. It doesn't follow from what we know.
D is definitely not true. It doesn't follow from what we know.
E is true. As x grows larger, f(x) goes to 2
F is false. For instance, f(x) = 2 + sin(x)/x. When x = pi * k, f(x) = 2.
G is false. It doesn't follow from what we know.