Use the binomial expansion to expand

$(16+2v{)}^{-\frac{1}{2}}|v|<8$

in ascending powers of $v$, up to and including the term in $v^2$, giving each coefficient as a fully simplified fraction.

The pressure $P$ in a pneumatic cylinder is modeled by the function

$P(v)=\frac{12+kv}{\sqrt{16+2v}}wherekis\; a\; constant\; and|v|<8$

Given that the series expansion of $P(v)$, in ascending powers of $v$, is

$3+\frac{9}{16}v+q{v}^2+\dots whereqis\; a\; constant$

find the value of $k$,

find the value of $q$.