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Evaluate lim(x to 0) (sqrt(1+x^(3))-sqrt...

Evaluate `lim_(x to 0) (sqrt(1+x^(3))-sqrt(1-x^(3)))/(x^(2))`

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Verified by Experts

Given, `underset(xto0)"lim"(sqrt(1+x^(3))-sqrt(1-x^(3)))/(x^(2))=underset(xto0)"lim"(sqrt(1+x^(2))-sqrt(1-x^(3)))/(x^(2)).(sqrt(1+x^(3))+sqrt(1-x^(3)))/(sqrt(1+x^(3))+sqrt(1-x^(3)))`
`=underset(xto0)"lim"((1+x^(3))-(1-x^(3)))/(x^(2)(sqrt(1+x^(3)) + sqrt(1-x^(3))))`
`=underset(xto0)"lim"(2x^(3))/(x^(2)(sqrt(1+x^(3)))+sqrt(1-x^(3)))`
`=underset(xto0)"lim"(2x)/(sqrt(1+x^(3))+sqrt(1-x^(3)))`
=0
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