_ 2 1- ( 2 - ) is equal to

Step-by-step solution

Let x = 2 - . As 2 , x 0 . Substituting = 2 - x , we have = ( 2 - x) = x and = ( 2 - x) = x . The limit becomes _ x 0 1 - x x x . Using the identity 1 - x = 2 ^2( x 2 ) , the expression is _ x 0 2 ^2( x 2 ) x x . Dividing numerator and denominator by x^2 , we get _ x 0 2 ( (x/2) x )^2 x x = _ x 0 2 ( 1 2 (x/2) x/2 )^2 x x . Since _ x 0 x x = 1 , the limit is 2 (1/2)^2 1 = 2 4 = 1 2 . Answer: 1 2