`lim_(x->2)(((x^3-4x)/(x^3-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(sqrt(x)-sqrt(2)))^(-1))i s equal to`

`1/2`

2

1

none of these

Options

A. 1
B. `1//2`
C. 2
D. none of these

Answer

A

Explanation

`underset(xto2)lim[((x(x-2)(x+2))/((x-2)(x^(2)+2x+4)))^(-1)-((sqrt(x)"("sqrt(x)+sqrt(2")"))/("("sqrt(x)-sqrt(2")")"("sqrt(x)+sqrt(2")"))-(sqrt(2))/(sqrt(x)-sqrt(2)))^(-1)]`
`=underset(xto2)lim[(x^(2)+2x+4
)/(x(x+2))-((sqrt(x)-sqrt(2))/(sqrt(x)-sqrt(2)))^(-1)]`
`=underset(xto2)lim[(x^(2)+2x+4)/(x(x+2))-1]=12/8-1=1/2`