= Solution
Regard the bifunctor as $D^{(2)}:K\to[J,\mathcal C]$. Its pointwise <categorical limit> $E=\lim_kD^{(2)}k$ satisfies
$$
E(j)=\lim_kD(j,k),
$$
with its action on <morphisms> obtained by the construction in part (a). Applying the limit-preservation result from part (d) gives
$$
\boxed{\lim_j\lim_kD(j,k)
=\lim_J E\cong\lim_k\bigl(\lim_JD^{(2)}k\bigr)
=\lim_k\lim_jD(j,k).}
$$
The comparison <isomorphism> is canonical relative to the chosen <categorical limit> cones: it is the unique <morphism> identifying all the projections to $D(j,k)$. This proves \b[<commutation of iterated categorical limits>], including an empty $J$ or $K$. Equivalently, both iterated constructions have the <universal property> of the <categorical limit> of $D$ on $J\times K$.
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