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Evaluate lim(xto-oo)[(x^(4)sin((1)/(x))+...

Evaluate `lim_(xto-oo)[(x^(4)sin((1)/(x))+x^(2))/((1+|x|^(3)))].`

Text Solution

Verified by Experts

`underset(xtooo)lim[(x^(4)sin((1)/(x))+x^(2))/((1-\x^(3)))]" "`(as x is negative)
`=underset(xtooo)lim[(xsin((1)/(x))+1/x)/(1/x^(3)-1)]`
`underset(xtooo)lim[(sin((1)/(x))/((1)/x)+(1)/(x))/((1)/(x^(3))-1)]`
`=(1+0)/(0-1)=-1`
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