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Function whose jump (non-negative differ...

Function whose jump (non-negative difference of LHL and RHL) of discontinuity is greater than or equal to one. Is/are

A

`f(x) = {{:((e^(1//x)+1)/(e^(1//x)-1)",",x lt 0),((1-cos x)/(x)",",x gt 0):}`

B

`g(x) = {{:((x^(1//3)-1)/(x^(1//2)-1)",",x gt 1),((log x)/(x-1)",",(1)/(2) lt x lt 1):}`

C

`u(x)={{:((sin^(-1)2x)/(tan^(-1)3x)",",x in [0, (1)/(2)]),((|sin x|)/(x)",",x lt 0):}`

D

`v(x) = {{:(log_(3)(x+2)",",x gt 2),(log_(1//2)(x^(2)+5)",",x lt 2):}`

Text Solution

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The correct Answer is:
A, C
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