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Evaluate lim(xtooo) ((7x^(2)+1)/(5x^(2)-...

Evaluate `lim_(xtooo) ((7x^(2)+1)/(5x^(2)-1))^((x^(5))/(1-x^(3))).`

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`underset(xtooo)lim(7x^(2)+1)/(5x^(2)-1)=underset(xtooo)lim(7+(1)/(x^(2)))/(5-(1)/(x^(2)))=7/5`
`=underset(xtooo)lim(x^(5))/(1-x^(3))=underset(xtooo)lim(x^(2))/((1)/(x^(3))-1)=-oo`
`:." "underset(xtooo)lim((7x^(2)+1)/(5x^(2)-1))^((x^(5))/(1-x^(3)))=underset(xtooo)lim((7x^(2)+1)/(5x^(2)-1))^((x^(5))/(1-x^(3)))`
`=((7)/(5))^(-oo)=0`
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