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Math Help - Help Needed with Advanced Limits # 3

  1. #1
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    Help Needed with Advanced Limits # 3

    I was wondering if someone could help me with the problems within the picture:




    I am in dire need of a step by step explanation as I answered this as -1 and was incorrect
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  2. #2
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    couldn't f be a radical like this (-x+1)/(x-1) so that the horizontal asymptote would be y =-1 and so the derivative of that function would be 0 so the limit of the derivative would also be zero. I think I got. Well, I hope so. Can someone confirm this please
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  3. #3
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    Quote Originally Posted by Some1Godlier View Post
    couldn't f be a radical like this (-x+1)/(x-1) so that the horizontal asymptote would be y =-1 and so the derivative of that function would be 0 so the limit of the derivative would also be zero. I think I got. Well, I hope so. Can someone confirm this please
    You are right - more or less:

    1. The example you gave is a constant function with a hole at x = 1. Better use f(x)=\dfrac{1-x}x (as an example of course!)

    2. If an asymptote y = -1 exists then the function can be replaced by f(x) = -1 for very large values of x.

    3. If f(x) = -1 then f'(x) = 0
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