Question 847201
lim      {{{(sqrt(1+x) - 1)/log(1+x)}}}
x->0 

Use L'hopital rule.

Derivative of numerator is {{{1/(2*sqrt(1+x))}}}
Derivative of denominator is {{{1/(x+1)}}}

Plugging in 0 for numerator gives 1/2
Plugging in 0 for denominator gives 1.

{{{(1/2)/1}}} =  1/2