If f (x)= 1+ x (1-x)^2 , for x 1 is continuous at x=1 , then f (1) is equal to

Step-by-step solution

aligned f (x) & = 1+ x (1-x)^2 f (1) & = _ x 1 f (x) & = _ x 1 1+ x (1-x)^2 aligned aligned & Put 1-x= h & 1- h =x & As x 1, ~h 0 & aligned f (1) & = _ h 0 1+ (1- h ) h ^2 = & _ h 0 1+ ( - h) h ^2 = & _ h 0 1- h h ^2 = & _ h 0 2 ^2 ~h 2 ~h ^2 = & 2 _ h 0 ^2 h 2 ^2 h^2 4 4 = & 2 4 _ h 0 ( h 2 h 2 )^2 f (1) & = 2 aligned aligned