Find: \(\displaystyle\lim_{{{t}\to\infty}}{\left[{e}^{{-{t}}}{\int_{{0}}^{{t}}}{\int_{{0}}^{{t}}}{\frac{{{e}^{{x}}-{e}^{{y}}}}{{{x}-{y}}}}{\left.{d}{x}\right.}{\left.{d}{y}\right.}\right]}\)

Yaritza Estrada

Yaritza Estrada

Answered question

2022-04-05

Find:
limt[et0t0texeyxydxdy]

Answer & Explanation

Ouhamiptkg

Ouhamiptkg

Beginner2022-04-06Added 18 answers

Let
F(y,t)=0texeyxydx
Then your G(t) is
G(t)=0tF(y,t)dy
Then
G(t)=F(t,t)+0tFt(y,t)dy
=0texetxtdx+0teteytydy

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