The value of `("lim")_(xvec2)(2^x+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))i s` 16 (b) 8 (c) 4 (d) 2

Options

A. ` 4 sqrt 2 `
B. ` 8`
C. ` 6`
D. `4 sqrt 3 `

Answer

B

Explanation

`{:(Lim),(x to 2):} (2^(x) + 2^(3-x)-6)/(sqrt(2^(-x)) - 2^(1-x))`
`= {:(lim),(x to 2):} (2^(x) .In x- 2^(3-x) In2)/((2(-x)/(2) In.2)/(2) + 2^(1-x).In 2),` using L,H rule
` = {:(Lim),(x to2):} (2^(x) - 2^(3-x))/(2^(1-x) - 2^((-x)/(2) -1)) = (4-2)/((1)/(2) - (1)/(4)) =8`