How to show that \(\displaystyle\lim_{{{p}\to{0}}}{\left({\frac{{{p}{e}^{{{2}{t}{p}}}}}{{{1}-{e}^{{{2}{t}{p}}}{\left({1}-{p}\right)}}}}\right)}^{{k}}\)

Heather Dickson 2022-04-09 Answered
How to show that
limp0(pe2tp1e2tp(1p))k
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Answers (1)

ze2m1ingkdvu
Answered 2022-04-10 Author has 16 answers
Have you tried l'Hospital's rule?
limp0pe2tp1e2tp(1p)=limp0e2tp+p(2t)e2tpe2tp(1p)(2t)e2tp=limp01+2tp1(1p)(2t)=112t
Just use the product rule and the case k=1 then
Hope that helps,
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