Question 1044766
{{{lim(x->0, (10^x-5^x-2^x+1)/x^2) }}}

= {{{lim(x->0, (ln10*10^x-ln5*5^x-ln2*2^x)/(2x))}}}

= {{{lim(x->0, ((ln10)^2*10^x-(ln5)^2*5^x-(ln2)^2*2^x)/2)}}}.

The last expression doesn't lead to an indeterminate form and so direct substitution of x = 0 gives...

{{{highlight(((ln10)^2-(ln5)^2-(ln2)^2)/2))}}}.