If the function f is continuous at x = , where f(x) = 1 - [7(x - )] 5(x - )^2 , for x , then f( ) =

Step-by-step solution

Since the function f(x) is continuous at x = , f( ) = _ x f(x) . Substituting t = x - , as x , t 0 . f( ) = _ t 0 1 - (7t) 5t^2 Using the identity 1 - = 2 ^2 ( 2 ) : f( ) = _ t 0 2 ^2 ( 7t 2 ) 5t^2 f( ) = 2 5 _ t 0 ( ( 7t 2 ) t )^2 f( ) = 2 5 ( 7 2 )^2 _ t 0 ( ( 7t 2 ) 7t 2 )^2 Since _ 0 = 1 : f( ) = 2 5 49 4 1 = 49 10 Answer: 49 10