Proving the Limit of a Parabola Delta Function

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The discussion centers on proving the limit of an integral involving a parabola that approaches a delta function as k approaches infinity. The integral is defined as L = lim (k→∞) ∫[-3/(4k), 3/(4k)] f(x)[-16k^3/9 x^2 + k] dx, which is believed to converge to f(0). Participants debate the properties of the parabola, its roots, and the area under the curve, asserting that it behaves like a delta function. They also explore the implications of using different functions f(x) and the conditions under which the limit holds, noting that continuity and differentiability at zero are crucial. The conversation highlights the complexity of establishing the delta function relationship and the need for careful consideration of function properties.
  • #31
Looks good to me. :smile:

As long as f is continuous, and the area beneath the curves formed by each member in your sequence equals 1, then this argument really shows that ANY such sequence is good enough to represent the delta function(al).
 

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