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Thread: Limits; (7 - x) / (x - 7) as x approaches 7: How do I SHOW that it's -1?

  1. #1

    Limits; (7 - x) / (x - 7) as x approaches 7: How do I SHOW that it's -1?

    Hello, all. I am trying to solve a limit question and although I am aware of the correct answer, I'm not quite sure how to arrive at it.

    For x approaches 7, (7 - x) / (x - 7)

    I know the answer is (-1), but I am not sure how to arrive there. It seems to me that both terms would cancel out and the answer would be 1.

    Thanks in advance for any replies!

  2. #2
    Elite Member
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    Quote Originally Posted by BusCalc View Post
    Hello, all. I am trying to solve a limit question and although I am aware of the correct answer, I'm not quite sure how to arrive at it.

    For x approaches 7, (7 - x) / (x - 7)

    I know the answer is (-1), but I am not sure how to arrive there. It seems to me that both terms would cancel out and the answer would be 1.

    Thanks in advance for any replies!
    Hint:

    x - 7 = -1 * (7 - x)
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
    Quote Originally Posted by Subhotosh Khan View Post
    Hint:

    x - 7 = -1 * (7 - x)
    Ahh, I see my mistake. I treated (7 - x) as though x were positive. So the (-1) is used to swap the signs of x and 7.

    Thank you for taking the time to help me out! I really appreciate it.

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