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Evaluate lim(xto0) (sinx-x)/(x^(3))....

Evaluate `lim_(xto0) (sinx-x)/(x^(3)).`

Text Solution

Verified by Experts

`underset(xto0)lim(sinx-x)/(x^(3))" "`(0/0" from")
`=underset(xto0)lim((x-(x^(3))/(3!)+x^(5)/(5!)-...)-x)/(x^(3))`
`=underset(xto0)lim[-(1)/(3!)+x^(2)/(5!)-... ]=(-1)/(3!)=(-1)/(6)`
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