Notice that
1 - 1/x
x - 1 x + sin
x x +
1 1 + 1/x
=
<
<
=
(for large x)
1 +
1/x x +
1 x + cos
x x -
1 1 - 1/x
Now the left and right hand side both approach 1 as a approaches infinity. The squeeze theorem implies that
