The value of f(x)= _ x 0 ( 8^x+2^x+4^x 3 )^ 2 / x , then f(x)^ equals to

Step-by-step solution

y= _ x 0 ( 8^x+2^x+4^x 3 )^ 2 / x aligned & y= _ x 0 2 x ( 8^x+2^x+4^x 3 ) & =2 _ x 0 1 x [ (8^x+2^x+4^x )- 3 ] aligned =2 _ x 0 [ (8^x+2^x+4^x )- 3 ] x [ 0 0 . form ] On applying L' Hospital rule, we get aligned & =2 _ x 0 [8^x 8+2^x 2+4^x 4 ] 8^x+2^x+4^x & =2 [ 8+ 2+ 4 3 ] aligned = 2 3 [3 2+ 2+2 2] [ (m)^n=n m ] aligned & = 2 3 6 2 & y=4 2= 16 y=16 aligned