Evaluate Limit of Step Function

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

  1. nycmathguy

    nycmathguy

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    Calculus
    Section 2.3

    I want to see the graph.
    For part (b), I need (ii) and (iii) only.
    Yes, part (c) is needed.

    Screenshot_20220503-184619_Samsung Notes.jpg
     
    nycmathguy, May 5, 2022
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  2. nycmathguy

    MathLover1

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    a.
    [​IMG]

    (i) upload_2022-5-4_21-17-39.gif

    (ii) upload_2022-5-4_21-18-36.gif

    (iii) upload_2022-5-4_21-19-32.gif

    (iv) upload_2022-5-4_21-20-11.gif
     
    MathLover1, May 5, 2022
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  3. nycmathguy

    nycmathguy

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    nycmathguy, May 5, 2022
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  4. nycmathguy

    MathLover1

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    The range of f(x)=[[cos x]], − π<=x< =π,where [[ ]] represent greatest integer function less than or equal to x is:

    cos[x]=cos(−1)=cos1
    cos[x]=cos(0)=1

    Required range={cos1,1}
     
    MathLover1, May 5, 2022
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  5. nycmathguy

    nycmathguy

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    I understand it is the Greatest Integer Function aka the Step Function. I thought the graph of the step function is like a ladder. No? I had no idea that this function can actually form the graph of a parabola.
     
    nycmathguy, May 5, 2022
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