Question

 lim    ln(1+2x) / ln(1+x) =??
x->0 


PS: chiar nu iteleg.

Answer 1

Cu ajutorul limitelor remarcabile:
...=lim (ln(x+2x)/2x) aceasta de inmultit cu 2x; totul supra (ln(1+x)/x) de imnultit cu x=lim (ln(1+2x)/2x)*2 supra (ln(1+x)*1=1*2/1*1=2

Answer 2

     
$Aplicam \,\,\, formula:\,\,\, \frac{ log_{c}b}{ log_{c}a} = log_{a}b \,\,\,si\,\,\,formula: \,\,\, log_{a}1=0 \\ \\ Lim_{x->o} \frac{ln(1+2x)}{ln(1+x)} = Lim_{x->o}log_{(1+x)}(1+2x)= log_{1}1=0$