Starting from the series given in the formulae booklet, show that the general term of the Maclaurin series for
$$\frac { \sin x } { x } - \cos x$$
is
$$( - 1 ) ^ { r + 1 } \frac { 2 r } { ( 2 r + 1 ) ! } x ^ { 2 r }$$
11
Show that
$$\lim _ { x \rightarrow 0 } \left[ \frac { \frac { \sin x } { x } - \cos x } { 1 - \cos x } \right] = \frac { 2 } { 3 }$$