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

Heather Dickson

Answered question

2022-04-09

How to show that
limp0(pe2tp1e2tp(1p))k

Answer & Explanation

ze2m1ingkdvu

ze2m1ingkdvu

Beginner2022-04-10Added 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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