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Question Number 184378 by Ml last updated on 05/Jan/23

lim_(x→∞)  (−ln((21)/(10)))^(2x) =?

limx(ln2110)2x=?

Answered by SEKRET last updated on 05/Jan/23

0

0

Commented by Ml last updated on 05/Jan/23

solution

solution

Answered by JDamian last updated on 05/Jan/23

∞ wrong

wrong

Commented by Ml last updated on 05/Jan/23

solution

solution

Answered by Frix last updated on 06/Jan/23

let −ln ((21)/(10)) =b  −1<b<0∧x>0 ⇒  b=∣b∣e^(iπ)  ⇒ b^(2x) =∣b∣^(2x) e^(2πxi)   ∣b∣<1 ⇒ lim_(x→∞)  ∣b∣^(2x)  =0  e^(2πxi) =cos 2πx +i sin 2πx  −1≤cos 2πx ≤1 ∧ −1≤sin 2πx ≤1 ⇒  lim ∣b∣^(2x) e^(2πxi)  =0+0i=0

letln2110=b1<b<0x>0b=∣beiπb2x=∣b2xe2πxib∣<1limxb2x=0e2πxi=cos2πx+isin2πx1cos2πx11sin2πx1limb2xe2πxi=0+0i=0

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