Calculus Limits?

Please answer and explain which of the follow are true for the given limit.

Update:

Selecting Option E ONLY is marked incorrect.

Selecting Options A, B & E is marked incorrect.

What is the answer :(

Update 2:

Options A & E are the answers to this given question. Thanks to everyone for their contributions.

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2 Answers

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  • TomV
    Lv 7
    10 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.

    Ans:

    B, E

    • Commenter avatarLogin to reply the answers
  • 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.

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