If f (x)= 4 x^4 [1- x 2 - x 4 + x 2 x 4 ] is continuous at x=0 , then f (0) is

Step-by-step solution

aligned f(x) & = 4 x^4 [1- x 2 - x 4 + x 2 x 4 ] & = 4 x^4 [ (1- x 2 )- x 4 (1- x 2 ) ] & = 4 x^4 [ (1- x 2 ) (1- x 4 ) ] aligned f (x) is continuous at x=0...[Given] . aligned (0) & = _ x 0 f (x) & = _ x 0 4 x^4 (1- x 2 ) (1- x 4 ) & =4 _ x 0 ( 2 ^2 x 4 x^2 ) ( 2 ^2 x 8 x^2 ) & =16 _ x 0 ( ^2 x 4 x^2 16 ) 1 16 _ x 0 ( ^2 x 8 x^2 64 ) 1 64 & =16 1 16 1 64 _ x 0 ( x 4 x 4 )^2 _ x 0 ( x 8 x 8 )^2 & = 1 64 1 1 & = 1 64 aligned