Does f ' (0) Exists?

Discussion in 'Calculus' started by nycmathguy, Jun 5, 2022.

  1. nycmathguy

    nycmathguy

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    Calculus
    Section 2.7

    Screenshot_20220605-184125_Samsung Notes.jpg

    Can you do 57? I will then do 58 using your reply as a guide.
     
    nycmathguy, Jun 5, 2022
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  2. nycmathguy

    MathLover1

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    57.
    given:

    [​IMG]

    f'(a)= upload_2022-6-5_19-31-36.gif

    a=0

    f'(0)= upload_2022-6-5_19-32-22.gif


    f'(0)=lim(h*sin(1/h))/h as h->0

    f'(0)=lim(sin(1/h)) as h->0

    f'(0)=lim(sin(1/0)) -> function oscillating no matter how far we go

    so, limit f'(0) DNE
     

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    MathLover1, Jun 6, 2022
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  3. nycmathguy

    nycmathguy

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    What do you mean by h tends to a box or square?
     
    nycmathguy, Jun 6, 2022
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  4. nycmathguy

    MathLover1

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    where do you see that "h tends to a box or square"?
    ah, I see now on the image above
    I was using wolfram alpha and didn't noticed it made a square instead of a

    I said h->a

    upload_2022-6-6_11-13-31.gif
     
    Last edited: Jun 6, 2022
    MathLover1, Jun 6, 2022
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  5. nycmathguy

    nycmathguy

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    Much better.
     
    nycmathguy, Jun 7, 2022
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