1.
1-x
> exp( -x/( 1-x ) )
( -1 < x < 1 ) : Q > Q1
exp( -x/( 1-x ) )
= 1/exp( x/( 1-x ) )
< 1/( 1+x/( 1-x ) )
= 1-x
2.
1-x
> exp( -x/( 1-x )+( 1/2 )( x^2/( 1-x^2 ) ) )
( -1 < x < 1 ) : Q > Q2
exp( -x/( 1-x )+( 1/2 )( x^2/( 1-x^2 ) ) )
< 1/( 1+( x/( 1-x )-( 1/2 )( x^2/( 1-x^2 ) ) )
= ( 1-x^2 )/( 1+x-x^2/2 )
= 1-x
q.e.d.
Remark :
lnQ1/( -2√t ) > π > lnQ2/( -2√t ) > lnQ/( -2√t )