If |x| is so small that x^2 and higher powers of x may be neglected, then the approximate value of 4+x + [3] 8-x (1- 2 x 3 )^ 3 2 when x= 6 25 is

Step-by-step solution

Using binomial expansions and neglecting x^2 and higher powers, we get aligned [2 (1+ x 4 )^ 1 2 +2 (1- x 8 )^ 1 3 ] (1- 2 x 3 )^ 3 2 =2 [1+ 1 2 x 4 +1- 1 3 x 8 ] (1- 2 x 3 )^ - 3 2 =2 [2+ x 8 - x 24 ] [1- 3 2 ( -2 x 3 ) ] =2 [2+ 2 x 24 ][1+x] aligned aligned & =2 [2+ x 12 ][1+x]=2 [2+2 x+ x 12 ] & =2 [2+ 25 x 12 ] aligned When, x= 6 25 =2 [2+ 25 12 6 25 ]=2 [2+ 1 2 ]=2 5 2 =5