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The value of underset(xto2)lim(2^(x)+2^(...

The value of `underset(xto2)lim(2^(x)+2^(3-x)-6)/(sqrt(2^(-x))-2^(1-x))" is "`

A

` 4 sqrt 2 `

B

` 8`

C

` 6`

D

`4 sqrt 3 `

Text Solution

Verified by Experts

The correct Answer is:
B
`{:(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`
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