How is \lim_{h \to 0} \frac {3^h-1} {h}=\ln3 evaluated?

Kailey Perez

Kailey Perez

Answered question

2022-04-21

How is
limh03h1h=ln3
evaluated?

Answer & Explanation

Jocelynn Meyer

Jocelynn Meyer

Beginner2022-04-22Added 9 answers

The result can also be obtained using ab{ex,dx}=ebea (for all a,bR). Indeed, for any h0 it holds
{3h1}h=0(ln3)h{eu,du}h,
and hence (since xex is continuous and e0=1
limh03h1h=limh00(ln3)h1duh
=limh0(ln3)hh
=ln3
Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-30Added 2605 answers

Answer is given below (on video)

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