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I Do limit and differential operators commute?

  1. Feb 16, 2017 #1
    In general I'm wondering if

    [tex]\lim_{x\to0} \left[\frac{d}{dy} \frac{d}{dx} f(x,y)\right] = \frac{d}{dy} \left[\lim_{x\to0} \frac{d}{dx} f(x,y)\right][/tex]

    holds true for all f(x,y). Thanks.
  2. jcsd
  3. Feb 16, 2017 #2


    Staff: Mentor

  4. Feb 16, 2017 #3
    No, not exactly. My f(x,y) is a huge compound function and it's a hassle to differentiate with respect to both variables and then take the limit, as opposed to differentiating by x, setting the limit and then differentiating (the now simpler function) by y.
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