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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

`4sqrt(2)`

B

`8`

C

`6`

D

`4sqrt(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
`Lim_(x to 2) (2^x + 2^(3-x)-6)/(sqrt2^(-x) - 2^(1-x))`
`=Lim_(x to 2) (2^x.ln x-2^(3-x) ln2)/(((2^(-x/2)ln2)/2)+2^(1-x) ln2)` using L.H rule
`=Lim_(x to 2) (2^x -2^(3-x))/(2^(1-x)-2^((-x)/2)-1)=(4-2)/(1/2-1/4)=8`
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