We have, $f(x)=3 x^{10}-7 x^{8}+5 x^{6}-21 x^{3}+3 x^{2}-7$
$\therefore \quad f(1-h)=3(1-h)^{10}-7(1-h)^{8}$
$+5(1-h)^{6}-21\left(1-h^{3}+3(1-h)^{2}-7\right.$
$=3\left(1-10 h+45 h^{2}-120 h^{3}+\ldots \ldots+h^{10}\right)$
$-7\left(1-8 h+28 h^{2}-56 h^{3}+\ldots . .+h^{8}\right)$
$+5\left(1-6 h+15 h^{2}-20 h^{3}+\ldots . .+h^{6}\right)$
$-21\left(1-3 h+3 h^{2}-h^{3}\right)$
$+3\left(1-2 h+h^{2}\right)-7$
$\Rightarrow f(1-h)=-24+53 h+h^{2}(-46)+h^{3}(-47)+\ldots$
and $\quad f(1)=-24$
$\therefore \quad \lim _{h \rightarrow 0} \frac{f(1-h)-f(1)}{h^{3}+3 h}$
$=\lim _{h \rightarrow 0} \frac{-24+53 h+h^{2}(-46)+h^{3}(-47)+\ldots-(-24)}{h\left(h^{2}+3\right)}$
$=\lim _{h \rightarrow 0} \frac{53 h+h^{2}(-46)+h^{3}(-47)+\ldots}{h\left(h^{2}+3\right)}$
$=\lim _{h \rightarrow 0} \frac{53+h(-46)+h^{2}(-47)+\ldots}{h^{2}+3}=\frac{53}{3}$