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lim(x to 2) (2^(x) + 2^(2 -x) - 5)/((1)/...

`lim_(x to 2) (2^(x) + 2^(2 -x) - 5)/((1)/(sqrt(2^(x))) + lambda (2)^(1 - x)) (lambda in R)` has non zero value, which can be

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The correct Answer is:
12
For `lambda = - 1` we get, form
(for `lambda != - 1`, limiting value is 0)
Applying LH Rule.
`:.underset(x to 2)("lim") (2^(x) log 2 - 2^(2 - x). Log^(2))/(2^(x//2) log 2 ((-(1)/(2)) + 2^(1 - x) log 2) lambda = - 1`
`underset((x to 2)("lim") (2^(x) - 2^(2 - x))/(-(2)/(2)^(-(x)/(2)) + 2^(1 - x)) = (4 - 1)/(-(1)/(4) + (1)/(2)) = (3)/((1)/(4)) = 12`
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