Question 1105090
You may want a 2nd opinion.  Here is what I get:

Lim x—>0 {{{   (f(x)/(Ax^4+Bx^3)) = C }}}   A,B,C constants

Lim x—>0 {{{  (f(x)/x^2) * (1/(Ax^2+Bx)) }}} = C
Lim x—>0 {{{  (f(x)/x^2) }}} * Lim x—>0 {{{  (1/(Ax^2+Bx)) }}} = C
Lim x—>0 {{{  (f(x)/x^2) }}} = C / ( Lim x—>0 {{{  (1/(Ax^2+Bx)) }}} )

The RHS denominator goes off to infinity, so C/denominator —> 0
Lim x—>0 {{{ highlight(  (f(x)/x^2)  = 0 )  }}}