Let f (x) = (1- x)2 sin2 x + x2 for all x Î IR, and let
1
2( 1)
( ) ln ( )
1
- = -
+
x
t
g x t f t dt
t
for all x Î (1, ¥).
51. Consider the statements:
P : There exists some x Î such that f(x) + 2x = 2(1 + x2)
Q : There exists some x Î such that 2f(x) + 1 = 2x(1 + x)