If L-("lim")(xvec2)((10-x)^(1/3)-2)/(x-2...

If `L-("lim")_(xvec2)((10-x)^(1/3)-2)/(x-2),t h e nt h ev a l u eof|1(4L)|i s___`

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Verified by Experts

The correct Answer is:

`(3)`

`underset(xto2)lim((10-x)^(1//3)-2)/(x-2)=underset(hto0)lim((8-h)^(1//3)-2)/(h)" "("Put "x=2+h)`
`=underset(hto0)lim(2(1-(h)/(8))^(1//3)-2)/(h)=2underset(hto0)lim((1+(h)/(8))^(1//3)-1)/(h)`
`=2underset(hto0)lim(1-(1)/(3)(h)/(8)-1)/(h)=-(1)/(12)`

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