The value of `lim_(xto2) (((x^(3)-4x)/(x^(3)-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(sqrt(x)-sqrt(2)))^(-1))" is "`

Question

The value of `lim_(xto2) (((x^(3)-4x)/(x^(3)-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(sqrt(x)-sqrt(2)))^(-1))" is "`

The value of `lim_(xto2) (((x^(3)-4x)/(x^(3)-8))^(-1)-((x+sqrt(2x))/(x-2)-(sqrt(2))/(sqrt(x)-sqrt(2)))^(-1))" is "`
A. 1
B. `1//2`
C. 2
D. none of these

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - A
`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`