Limit Prove

Discussion in 'Calculus' started by nycmathguy, Apr 14, 2022.

  1. nycmathguy

    nycmathguy

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    Calculus
    Section 1.6

    This prove question is unclear to me.

    Screenshot_20220410-202943_Samsung Notes.jpg
     
    nycmathguy, Apr 14, 2022
    #1
  2. nycmathguy

    MathLover1

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    note: lim(f(x), x->0)=f(0)

    let us find the following limits:
    lim(f(x), x->0) and if x is a rational number, will be
    lim(x^2,x->0 ) =0^2=0
    upload_2022-4-13_20-46-32.gif

    lim(f(x)) as x->0 and if x is a irrational number, will be
    upload_2022-4-13_20-44-3.gif

    Since the limits above are same, it proves that lim(f(x), x->0) does exist
     

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    MathLover1, Apr 14, 2022
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  3. nycmathguy

    nycmathguy

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    Not too bad, honestly.
     
    nycmathguy, Apr 14, 2022
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