Find \lim_{x\rightarrow−\infty}\frac{\ln(1+3^x)}{\ln(1+2^x)}

widdonod1t

widdonod1t

Answered question

2022-01-21

Find limxln(1+3x)ln(1+2x)

Answer & Explanation

esfloravaou

esfloravaou

Beginner2022-01-21Added 43 answers

HINT:
zz+1log(1+z)z (1)
for z>1. Then, use the squeeze theorem.
NOTE 1:
We can prove the inequalities in (1) using standard tools, which dont
censoratojk

censoratojk

Beginner2022-01-22Added 46 answers

Notice,
limxln(1+3x)ln(1+2x)
substituting x=t, we get
limxln(1+3t)ln(1+2t)
limx(ln(1+3t)3tln(1+2t)2t)×2t3t
=(limxln(1+3t)3tlimxln(1+2t)2t)×limx(23)t
=11×(0)=0

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